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