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Simplifying (x + 2)(x + -6) = 5x2 + 10x Reorder the terms: (2 + x)(x + -6) = 5x2 + 10x Reorder the terms: (2 + x)(-6 + x) = 5x2 + 10x Multiply (2 + x) * (-6 + x) (2(-6 + x) + x(-6 + x)) = 5x2 + 10x ((-6 * 2 + x * 2) + x(-6 + x)) = 5x2 + 10x ((-12 + 2x) + x(-6 + x)) = 5x2 + 10x (-12 + 2x + (-6 * x + x * x)) = 5x2 + 10x (-12 + 2x + (-6x + x2)) = 5x2 + 10x Combine like terms: 2x + -6x = -4x (-12 + -4x + x2) = 5x2 + 10x Reorder the terms: -12 + -4x + x2 = 10x + 5x2 Solving -12 + -4x + x2 = 10x + 5x2 Solving for variable 'x'. Reorder the terms: -12 + -4x + -10x + x2 + -5x2 = 10x + 5x2 + -10x + -5x2 Combine like terms: -4x + -10x = -14x -12 + -14x + x2 + -5x2 = 10x + 5x2 + -10x + -5x2 Combine like terms: x2 + -5x2 = -4x2 -12 + -14x + -4x2 = 10x + 5x2 + -10x + -5x2 Reorder the terms: -12 + -14x + -4x2 = 10x + -10x + 5x2 + -5x2 Combine like terms: 10x + -10x = 0 -12 + -14x + -4x2 = 0 + 5x2 + -5x2 -12 + -14x + -4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -12 + -14x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(6 + 7x + 2x2) = 0 Factor a trinomial. -2((2 + x)(3 + 2x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-2, -1.5}
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