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Simplifying (5 + x) * 2 + -1(3x + -4)(5 + x) = 0 Reorder the terms for easier multiplication: 2(5 + x) + -1(3x + -4)(5 + x) = 0 (5 * 2 + x * 2) + -1(3x + -4)(5 + x) = 0 (10 + 2x) + -1(3x + -4)(5 + x) = 0 Reorder the terms: 10 + 2x + -1(-4 + 3x)(5 + x) = 0 Multiply (-4 + 3x) * (5 + x) 10 + 2x + -1(-4(5 + x) + 3x * (5 + x)) = 0 10 + 2x + -1((5 * -4 + x * -4) + 3x * (5 + x)) = 0 10 + 2x + -1((-20 + -4x) + 3x * (5 + x)) = 0 10 + 2x + -1(-20 + -4x + (5 * 3x + x * 3x)) = 0 10 + 2x + -1(-20 + -4x + (15x + 3x2)) = 0 Combine like terms: -4x + 15x = 11x 10 + 2x + -1(-20 + 11x + 3x2) = 0 10 + 2x + (-20 * -1 + 11x * -1 + 3x2 * -1) = 0 10 + 2x + (20 + -11x + -3x2) = 0 Reorder the terms: 10 + 20 + 2x + -11x + -3x2 = 0 Combine like terms: 10 + 20 = 30 30 + 2x + -11x + -3x2 = 0 Combine like terms: 2x + -11x = -9x 30 + -9x + -3x2 = 0 Solving 30 + -9x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -3x + -1x2) = 0 Factor a trinomial. 3((2 + -1x)(5 + x)) = 0 Ignore the factor 3.Subproblem 1
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 = 2Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {2, -5}
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