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Simplifying (x + 5)(x + -2) = (2x + 2)(x + -2) Reorder the terms: (5 + x)(x + -2) = (2x + 2)(x + -2) Reorder the terms: (5 + x)(-2 + x) = (2x + 2)(x + -2) Multiply (5 + x) * (-2 + x) (5(-2 + x) + x(-2 + x)) = (2x + 2)(x + -2) ((-2 * 5 + x * 5) + x(-2 + x)) = (2x + 2)(x + -2) ((-10 + 5x) + x(-2 + x)) = (2x + 2)(x + -2) (-10 + 5x + (-2 * x + x * x)) = (2x + 2)(x + -2) (-10 + 5x + (-2x + x2)) = (2x + 2)(x + -2) Combine like terms: 5x + -2x = 3x (-10 + 3x + x2) = (2x + 2)(x + -2) Reorder the terms: -10 + 3x + x2 = (2 + 2x)(x + -2) Reorder the terms: -10 + 3x + x2 = (2 + 2x)(-2 + x) Multiply (2 + 2x) * (-2 + x) -10 + 3x + x2 = (2(-2 + x) + 2x * (-2 + x)) -10 + 3x + x2 = ((-2 * 2 + x * 2) + 2x * (-2 + x)) -10 + 3x + x2 = ((-4 + 2x) + 2x * (-2 + x)) -10 + 3x + x2 = (-4 + 2x + (-2 * 2x + x * 2x)) -10 + 3x + x2 = (-4 + 2x + (-4x + 2x2)) Combine like terms: 2x + -4x = -2x -10 + 3x + x2 = (-4 + -2x + 2x2) Solving -10 + 3x + x2 = -4 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: -10 + 4 + 3x + 2x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Combine like terms: -10 + 4 = -6 -6 + 3x + 2x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Combine like terms: 3x + 2x = 5x -6 + 5x + x2 + -2x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -6 + 5x + -1x2 = -4 + -2x + 2x2 + 4 + 2x + -2x2 Reorder the terms: -6 + 5x + -1x2 = -4 + 4 + -2x + 2x + 2x2 + -2x2 Combine like terms: -4 + 4 = 0 -6 + 5x + -1x2 = 0 + -2x + 2x + 2x2 + -2x2 -6 + 5x + -1x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -6 + 5x + -1x2 = 0 + 2x2 + -2x2 -6 + 5x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + 5x + -1x2 = 0 Factor a trinomial. (-3 + x)(2 + -1x) = 0Subproblem 1
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 = 3Subproblem 2
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 = 2Solution
x = {3, 2}
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