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Simplifying (x + -3)(x + -2) = 42 Reorder the terms: (-3 + x)(x + -2) = 42 Reorder the terms: (-3 + x)(-2 + x) = 42 Multiply (-3 + x) * (-2 + x) (-3(-2 + x) + x(-2 + x)) = 42 ((-2 * -3 + x * -3) + x(-2 + x)) = 42 ((6 + -3x) + x(-2 + x)) = 42 (6 + -3x + (-2 * x + x * x)) = 42 (6 + -3x + (-2x + x2)) = 42 Combine like terms: -3x + -2x = -5x (6 + -5x + x2) = 42 Solving 6 + -5x + x2 = 42 Solving for variable 'x'. Reorder the terms: 6 + -42 + -5x + x2 = 42 + -42 Combine like terms: 6 + -42 = -36 -36 + -5x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -36 + -5x + x2 = 0 Factor a trinomial. (-4 + -1x)(9 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-4, 9}
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