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Simplifying (x + 3)(x + -2) = 2x + 6 Reorder the terms: (3 + x)(x + -2) = 2x + 6 Reorder the terms: (3 + x)(-2 + x) = 2x + 6 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) = 2x + 6 ((-2 * 3 + x * 3) + x(-2 + x)) = 2x + 6 ((-6 + 3x) + x(-2 + x)) = 2x + 6 (-6 + 3x + (-2 * x + x * x)) = 2x + 6 (-6 + 3x + (-2x + x2)) = 2x + 6 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) = 2x + 6 Reorder the terms: -6 + 1x + x2 = 6 + 2x Solving -6 + 1x + x2 = 6 + 2x Solving for variable 'x'. Reorder the terms: -6 + -6 + 1x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: -6 + -6 = -12 -12 + 1x + -2x + x2 = 6 + 2x + -6 + -2x Combine like terms: 1x + -2x = -1x -12 + -1x + x2 = 6 + 2x + -6 + -2x Reorder the terms: -12 + -1x + x2 = 6 + -6 + 2x + -2x Combine like terms: 6 + -6 = 0 -12 + -1x + x2 = 0 + 2x + -2x -12 + -1x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -12 + -1x + x2 = 0 Factor a trinomial. (-3 + -1x)(4 + -1x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
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 = 4Solution
x = {-3, 4}
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