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Simplifying (x + -2)(x + 1) * 2 + 6(x + 1) * 3 = 0 Reorder the terms: (-2 + x)(x + 1) * 2 + 6(x + 1) * 3 = 0 Reorder the terms: (-2 + x)(1 + x) * 2 + 6(x + 1) * 3 = 0 Reorder the terms for easier multiplication: 2(-2 + x)(1 + x) + 6(x + 1) * 3 = 0 Multiply (-2 + x) * (1 + x) 2(-2(1 + x) + x(1 + x)) + 6(x + 1) * 3 = 0 2((1 * -2 + x * -2) + x(1 + x)) + 6(x + 1) * 3 = 0 2((-2 + -2x) + x(1 + x)) + 6(x + 1) * 3 = 0 2(-2 + -2x + (1 * x + x * x)) + 6(x + 1) * 3 = 0 2(-2 + -2x + (1x + x2)) + 6(x + 1) * 3 = 0 Combine like terms: -2x + 1x = -1x 2(-2 + -1x + x2) + 6(x + 1) * 3 = 0 (-2 * 2 + -1x * 2 + x2 * 2) + 6(x + 1) * 3 = 0 (-4 + -2x + 2x2) + 6(x + 1) * 3 = 0 Reorder the terms: -4 + -2x + 2x2 + 6(1 + x) * 3 = 0 Reorder the terms for easier multiplication: -4 + -2x + 2x2 + 6 * 3(1 + x) = 0 Multiply 6 * 3 -4 + -2x + 2x2 + 18(1 + x) = 0 -4 + -2x + 2x2 + (1 * 18 + x * 18) = 0 -4 + -2x + 2x2 + (18 + 18x) = 0 Reorder the terms: -4 + 18 + -2x + 18x + 2x2 = 0 Combine like terms: -4 + 18 = 14 14 + -2x + 18x + 2x2 = 0 Combine like terms: -2x + 18x = 16x 14 + 16x + 2x2 = 0 Solving 14 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 8x + x2) = 0 Factor a trinomial. 2((7 + x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 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 = {-7, -1}
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