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Simplifying (x + 2)(x + -5) = (2x + 3)(x + -5) Reorder the terms: (2 + x)(x + -5) = (2x + 3)(x + -5) Reorder the terms: (2 + x)(-5 + x) = (2x + 3)(x + -5) Multiply (2 + x) * (-5 + x) (2(-5 + x) + x(-5 + x)) = (2x + 3)(x + -5) ((-5 * 2 + x * 2) + x(-5 + x)) = (2x + 3)(x + -5) ((-10 + 2x) + x(-5 + x)) = (2x + 3)(x + -5) (-10 + 2x + (-5 * x + x * x)) = (2x + 3)(x + -5) (-10 + 2x + (-5x + x2)) = (2x + 3)(x + -5) Combine like terms: 2x + -5x = -3x (-10 + -3x + x2) = (2x + 3)(x + -5) Reorder the terms: -10 + -3x + x2 = (3 + 2x)(x + -5) Reorder the terms: -10 + -3x + x2 = (3 + 2x)(-5 + x) Multiply (3 + 2x) * (-5 + x) -10 + -3x + x2 = (3(-5 + x) + 2x * (-5 + x)) -10 + -3x + x2 = ((-5 * 3 + x * 3) + 2x * (-5 + x)) -10 + -3x + x2 = ((-15 + 3x) + 2x * (-5 + x)) -10 + -3x + x2 = (-15 + 3x + (-5 * 2x + x * 2x)) -10 + -3x + x2 = (-15 + 3x + (-10x + 2x2)) Combine like terms: 3x + -10x = -7x -10 + -3x + x2 = (-15 + -7x + 2x2) Solving -10 + -3x + x2 = -15 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: -10 + 15 + -3x + 7x + x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: -10 + 15 = 5 5 + -3x + 7x + x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: -3x + 7x = 4x 5 + 4x + x2 + -2x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Combine like terms: x2 + -2x2 = -1x2 5 + 4x + -1x2 = -15 + -7x + 2x2 + 15 + 7x + -2x2 Reorder the terms: 5 + 4x + -1x2 = -15 + 15 + -7x + 7x + 2x2 + -2x2 Combine like terms: -15 + 15 = 0 5 + 4x + -1x2 = 0 + -7x + 7x + 2x2 + -2x2 5 + 4x + -1x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 5 + 4x + -1x2 = 0 + 2x2 + -2x2 5 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 4x + -1x2 = 0 Factor a trinomial. (5 + -1x)(1 + x) = 0Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {5, -1}
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