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Simplifying (w2 + w + -20)(w2 + 11w + 30) * 3 + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: (-20 + w + w2)(w2 + 11w + 30) * 3 + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: (-20 + w + w2)(30 + 11w + w2) * 3 + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms for easier multiplication: 3(-20 + w + w2)(30 + 11w + w2) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Multiply (-20 + w + w2) * (30 + 11w + w2) 3(-20(30 + 11w + w2) + w(30 + 11w + w2) + w2(30 + 11w + w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3((30 * -20 + 11w * -20 + w2 * -20) + w(30 + 11w + w2) + w2(30 + 11w + w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3((-600 + -220w + -20w2) + w(30 + 11w + w2) + w2(30 + 11w + w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3(-600 + -220w + -20w2 + (30 * w + 11w * w + w2 * w) + w2(30 + 11w + w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3(-600 + -220w + -20w2 + (30w + 11w2 + w3) + w2(30 + 11w + w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3(-600 + -220w + -20w2 + 30w + 11w2 + w3 + (30 * w2 + 11w * w2 + w2 * w2)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 3(-600 + -220w + -20w2 + 30w + 11w2 + w3 + (30w2 + 11w3 + w4)) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: 3(-600 + -220w + 30w + -20w2 + 11w2 + 30w2 + w3 + 11w3 + w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -220w + 30w = -190w 3(-600 + -190w + -20w2 + 11w2 + 30w2 + w3 + 11w3 + w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -20w2 + 11w2 = -9w2 3(-600 + -190w + -9w2 + 30w2 + w3 + 11w3 + w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -9w2 + 30w2 = 21w2 3(-600 + -190w + 21w2 + w3 + 11w3 + w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: w3 + 11w3 = 12w3 3(-600 + -190w + 21w2 + 12w3 + w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 (-600 * 3 + -190w * 3 + 21w2 * 3 + 12w3 * 3 + w4 * 3) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 (-1800 + -570w + 63w2 + 36w3 + 3w4) + (w2 + 2w + -24)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: -1800 + -570w + 63w2 + 36w3 + 3w4 + (-24 + 2w + w2)(w2 + 11w + 30) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: -1800 + -570w + 63w2 + 36w3 + 3w4 + (-24 + 2w + w2)(30 + 11w + w2) * 1 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms for easier multiplication: -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-24 + 2w + w2)(30 + 11w + w2) = (w2 + 2w + -24)(w2 + w + -20) * 3 Multiply (-24 + 2w + w2) * (30 + 11w + w2) -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-24(30 + 11w + w2) + 2w * (30 + 11w + w2) + w2(30 + 11w + w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1((30 * -24 + 11w * -24 + w2 * -24) + 2w * (30 + 11w + w2) + w2(30 + 11w + w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1((-720 + -264w + -24w2) + 2w * (30 + 11w + w2) + w2(30 + 11w + w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -264w + -24w2 + (30 * 2w + 11w * 2w + w2 * 2w) + w2(30 + 11w + w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -264w + -24w2 + (60w + 22w2 + 2w3) + w2(30 + 11w + w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -264w + -24w2 + 60w + 22w2 + 2w3 + (30 * w2 + 11w * w2 + w2 * w2)) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -264w + -24w2 + 60w + 22w2 + 2w3 + (30w2 + 11w3 + w4)) = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -264w + 60w + -24w2 + 22w2 + 30w2 + 2w3 + 11w3 + w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -264w + 60w = -204w -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -204w + -24w2 + 22w2 + 30w2 + 2w3 + 11w3 + w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -24w2 + 22w2 = -2w2 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -204w + -2w2 + 30w2 + 2w3 + 11w3 + w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -2w2 + 30w2 = 28w2 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -204w + 28w2 + 2w3 + 11w3 + w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: 2w3 + 11w3 = 13w3 -1800 + -570w + 63w2 + 36w3 + 3w4 + 1(-720 + -204w + 28w2 + 13w3 + w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + (-720 * 1 + -204w * 1 + 28w2 * 1 + 13w3 * 1 + w4 * 1) = (w2 + 2w + -24)(w2 + w + -20) * 3 -1800 + -570w + 63w2 + 36w3 + 3w4 + (-720 + -204w + 28w2 + 13w3 + 1w4) = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: -1800 + -720 + -570w + -204w + 63w2 + 28w2 + 36w3 + 13w3 + 3w4 + 1w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -1800 + -720 = -2520 -2520 + -570w + -204w + 63w2 + 28w2 + 36w3 + 13w3 + 3w4 + 1w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: -570w + -204w = -774w -2520 + -774w + 63w2 + 28w2 + 36w3 + 13w3 + 3w4 + 1w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: 63w2 + 28w2 = 91w2 -2520 + -774w + 91w2 + 36w3 + 13w3 + 3w4 + 1w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: 36w3 + 13w3 = 49w3 -2520 + -774w + 91w2 + 49w3 + 3w4 + 1w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Combine like terms: 3w4 + 1w4 = 4w4 -2520 + -774w + 91w2 + 49w3 + 4w4 = (w2 + 2w + -24)(w2 + w + -20) * 3 Reorder the terms: -2520 + -774w + 91w2 + 49w3 + 4w4 = (-24 + 2w + w2)(w2 + w + -20) * 3 Reorder the terms: -2520 + -774w + 91w2 + 49w3 + 4w4 = (-24 + 2w + w2)(-20 + w + w2) * 3 Reorder the terms for easier multiplication: -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(-24 + 2w + w2)(-20 + w + w2) Multiply (-24 + 2w + w2) * (-20 + w + w2) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(-24(-20 + w + w2) + 2w * (-20 + w + w2) + w2(-20 + w + w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3((-20 * -24 + w * -24 + w2 * -24) + 2w * (-20 + w + w2) + w2(-20 + w + w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3((480 + -24w + -24w2) + 2w * (-20 + w + w2) + w2(-20 + w + w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -24w + -24w2 + (-20 * 2w + w * 2w + w2 * 2w) + w2(-20 + w + w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -24w + -24w2 + (-40w + 2w2 + 2w3) + w2(-20 + w + w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -24w + -24w2 + -40w + 2w2 + 2w3 + (-20 * w2 + w * w2 + w2 * w2)) -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -24w + -24w2 + -40w + 2w2 + 2w3 + (-20w2 + w3 + w4)) Reorder the terms: -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -24w + -40w + -24w2 + 2w2 + -20w2 + 2w3 + w3 + w4) Combine like terms: -24w + -40w = -64w -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -64w + -24w2 + 2w2 + -20w2 + 2w3 + w3 + w4) Combine like terms: -24w2 + 2w2 = -22w2 -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -64w + -22w2 + -20w2 + 2w3 + w3 + w4) Combine like terms: -22w2 + -20w2 = -42w2 -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -64w + -42w2 + 2w3 + w3 + w4) Combine like terms: 2w3 + w3 = 3w3 -2520 + -774w + 91w2 + 49w3 + 4w4 = 3(480 + -64w + -42w2 + 3w3 + w4) -2520 + -774w + 91w2 + 49w3 + 4w4 = (480 * 3 + -64w * 3 + -42w2 * 3 + 3w3 * 3 + w4 * 3) -2520 + -774w + 91w2 + 49w3 + 4w4 = (1440 + -192w + -126w2 + 9w3 + 3w4) Solving -2520 + -774w + 91w2 + 49w3 + 4w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 Solving for variable 'w'. Reorder the terms: -2520 + -1440 + -774w + 192w + 91w2 + 126w2 + 49w3 + -9w3 + 4w4 + -3w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Combine like terms: -2520 + -1440 = -3960 -3960 + -774w + 192w + 91w2 + 126w2 + 49w3 + -9w3 + 4w4 + -3w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Combine like terms: -774w + 192w = -582w -3960 + -582w + 91w2 + 126w2 + 49w3 + -9w3 + 4w4 + -3w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Combine like terms: 91w2 + 126w2 = 217w2 -3960 + -582w + 217w2 + 49w3 + -9w3 + 4w4 + -3w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Combine like terms: 49w3 + -9w3 = 40w3 -3960 + -582w + 217w2 + 40w3 + 4w4 + -3w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Combine like terms: 4w4 + -3w4 = 1w4 -3960 + -582w + 217w2 + 40w3 + 1w4 = 1440 + -192w + -126w2 + 9w3 + 3w4 + -1440 + 192w + 126w2 + -9w3 + -3w4 Reorder the terms: -3960 + -582w + 217w2 + 40w3 + 1w4 = 1440 + -1440 + -192w + 192w + -126w2 + 126w2 + 9w3 + -9w3 + 3w4 + -3w4 Combine like terms: 1440 + -1440 = 0 -3960 + -582w + 217w2 + 40w3 + 1w4 = 0 + -192w + 192w + -126w2 + 126w2 + 9w3 + -9w3 + 3w4 + -3w4 -3960 + -582w + 217w2 + 40w3 + 1w4 = -192w + 192w + -126w2 + 126w2 + 9w3 + -9w3 + 3w4 + -3w4 Combine like terms: -192w + 192w = 0 -3960 + -582w + 217w2 + 40w3 + 1w4 = 0 + -126w2 + 126w2 + 9w3 + -9w3 + 3w4 + -3w4 -3960 + -582w + 217w2 + 40w3 + 1w4 = -126w2 + 126w2 + 9w3 + -9w3 + 3w4 + -3w4 Combine like terms: -126w2 + 126w2 = 0 -3960 + -582w + 217w2 + 40w3 + 1w4 = 0 + 9w3 + -9w3 + 3w4 + -3w4 -3960 + -582w + 217w2 + 40w3 + 1w4 = 9w3 + -9w3 + 3w4 + -3w4 Combine like terms: 9w3 + -9w3 = 0 -3960 + -582w + 217w2 + 40w3 + 1w4 = 0 + 3w4 + -3w4 -3960 + -582w + 217w2 + 40w3 + 1w4 = 3w4 + -3w4 Combine like terms: 3w4 + -3w4 = 0 -3960 + -582w + 217w2 + 40w3 + 1w4 = 0 The solution to this equation could not be determined.
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