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Simplifying (3w + 2)(w + -5) = 12w + 8 Reorder the terms: (2 + 3w)(w + -5) = 12w + 8 Reorder the terms: (2 + 3w)(-5 + w) = 12w + 8 Multiply (2 + 3w) * (-5 + w) (2(-5 + w) + 3w * (-5 + w)) = 12w + 8 ((-5 * 2 + w * 2) + 3w * (-5 + w)) = 12w + 8 ((-10 + 2w) + 3w * (-5 + w)) = 12w + 8 (-10 + 2w + (-5 * 3w + w * 3w)) = 12w + 8 (-10 + 2w + (-15w + 3w2)) = 12w + 8 Combine like terms: 2w + -15w = -13w (-10 + -13w + 3w2) = 12w + 8 Reorder the terms: -10 + -13w + 3w2 = 8 + 12w Solving -10 + -13w + 3w2 = 8 + 12w Solving for variable 'w'. Reorder the terms: -10 + -8 + -13w + -12w + 3w2 = 8 + 12w + -8 + -12w Combine like terms: -10 + -8 = -18 -18 + -13w + -12w + 3w2 = 8 + 12w + -8 + -12w Combine like terms: -13w + -12w = -25w -18 + -25w + 3w2 = 8 + 12w + -8 + -12w Reorder the terms: -18 + -25w + 3w2 = 8 + -8 + 12w + -12w Combine like terms: 8 + -8 = 0 -18 + -25w + 3w2 = 0 + 12w + -12w -18 + -25w + 3w2 = 12w + -12w Combine like terms: 12w + -12w = 0 -18 + -25w + 3w2 = 0 Factor a trinomial. (-2 + -3w)(9 + -1w) = 0Subproblem 1
Set the factor '(-2 + -3w)' equal to zero and attempt to solve: Simplifying -2 + -3w = 0 Solving -2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3w = 0 + 2 -3w = 0 + 2 Combine like terms: 0 + 2 = 2 -3w = 2 Divide each side by '-3'. w = -0.6666666667 Simplifying w = -0.6666666667Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Solution
w = {-0.6666666667, 9}
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