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Simplifying (x + 4)(x + -4) = x2 + rx + t Reorder the terms: (4 + x)(x + -4) = x2 + rx + t Reorder the terms: (4 + x)(-4 + x) = x2 + rx + t Multiply (4 + x) * (-4 + x) (4(-4 + x) + x(-4 + x)) = x2 + rx + t ((-4 * 4 + x * 4) + x(-4 + x)) = x2 + rx + t ((-16 + 4x) + x(-4 + x)) = x2 + rx + t (-16 + 4x + (-4 * x + x * x)) = x2 + rx + t (-16 + 4x + (-4x + x2)) = x2 + rx + t Combine like terms: 4x + -4x = 0 (-16 + 0 + x2) = x2 + rx + t (-16 + x2) = x2 + rx + t Reorder the terms: -16 + x2 = rx + t + x2 Add '-1x2' to each side of the equation. -16 + x2 + -1x2 = rx + t + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + 0 = rx + t + x2 + -1x2 -16 = rx + t + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 = rx + t + 0 -16 = rx + t Solving -16 = rx + t Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1rx' to each side of the equation. -16 + -1rx = rx + -1rx + t Combine like terms: rx + -1rx = 0 -16 + -1rx = 0 + t -16 + -1rx = t Add '16' to each side of the equation. -16 + 16 + -1rx = 16 + t Combine like terms: -16 + 16 = 0 0 + -1rx = 16 + t -1rx = 16 + t Divide each side by '-1x'. r = -16x-1 + -1tx-1 Simplifying r = -16x-1 + -1tx-1 Reorder the terms: r = -1tx-1 + -16x-1
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