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