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Simplifying (x + -2)(x + 3) + 6x = 2x + 2 + -1x + -1x * x Reorder the terms: (-2 + x)(x + 3) + 6x = 2x + 2 + -1x + -1x * x Reorder the terms: (-2 + x)(3 + x) + 6x = 2x + 2 + -1x + -1x * x Multiply (-2 + x) * (3 + x) (-2(3 + x) + x(3 + x)) + 6x = 2x + 2 + -1x + -1x * x ((3 * -2 + x * -2) + x(3 + x)) + 6x = 2x + 2 + -1x + -1x * x ((-6 + -2x) + x(3 + x)) + 6x = 2x + 2 + -1x + -1x * x (-6 + -2x + (3 * x + x * x)) + 6x = 2x + 2 + -1x + -1x * x (-6 + -2x + (3x + x2)) + 6x = 2x + 2 + -1x + -1x * x Combine like terms: -2x + 3x = 1x (-6 + 1x + x2) + 6x = 2x + 2 + -1x + -1x * x Reorder the terms: -6 + 1x + 6x + x2 = 2x + 2 + -1x + -1x * x Combine like terms: 1x + 6x = 7x -6 + 7x + x2 = 2x + 2 + -1x + -1x * x Multiply x * x -6 + 7x + x2 = 2x + 2 + -1x + -1x2 Reorder the terms: -6 + 7x + x2 = 2 + 2x + -1x + -1x2 Combine like terms: 2x + -1x = 1x -6 + 7x + x2 = 2 + 1x + -1x2 Solving -6 + 7x + x2 = 2 + 1x + -1x2 Solving for variable 'x'. Reorder the terms: -6 + -2 + 7x + -1x + x2 + x2 = 2 + 1x + -1x2 + -2 + -1x + x2 Combine like terms: -6 + -2 = -8 -8 + 7x + -1x + x2 + x2 = 2 + 1x + -1x2 + -2 + -1x + x2 Combine like terms: 7x + -1x = 6x -8 + 6x + x2 + x2 = 2 + 1x + -1x2 + -2 + -1x + x2 Combine like terms: x2 + x2 = 2x2 -8 + 6x + 2x2 = 2 + 1x + -1x2 + -2 + -1x + x2 Reorder the terms: -8 + 6x + 2x2 = 2 + -2 + 1x + -1x + -1x2 + x2 Combine like terms: 2 + -2 = 0 -8 + 6x + 2x2 = 0 + 1x + -1x + -1x2 + x2 -8 + 6x + 2x2 = 1x + -1x + -1x2 + x2 Combine like terms: 1x + -1x = 0 -8 + 6x + 2x2 = 0 + -1x2 + x2 -8 + 6x + 2x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -8 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 3x + x2) = 0 Factor a trinomial. 2((-4 + -1x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -4Subproblem 2
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 = 1Solution
x = {-4, 1}
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