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Simplifying 3x(x + -2) + -1(x + 1)(x + -13) = 13 Reorder the terms: 3x(-2 + x) + -1(x + 1)(x + -13) = 13 (-2 * 3x + x * 3x) + -1(x + 1)(x + -13) = 13 (-6x + 3x2) + -1(x + 1)(x + -13) = 13 Reorder the terms: -6x + 3x2 + -1(1 + x)(x + -13) = 13 Reorder the terms: -6x + 3x2 + -1(1 + x)(-13 + x) = 13 Multiply (1 + x) * (-13 + x) -6x + 3x2 + -1(1(-13 + x) + x(-13 + x)) = 13 -6x + 3x2 + -1((-13 * 1 + x * 1) + x(-13 + x)) = 13 -6x + 3x2 + -1((-13 + 1x) + x(-13 + x)) = 13 -6x + 3x2 + -1(-13 + 1x + (-13 * x + x * x)) = 13 -6x + 3x2 + -1(-13 + 1x + (-13x + x2)) = 13 Combine like terms: 1x + -13x = -12x -6x + 3x2 + -1(-13 + -12x + x2) = 13 -6x + 3x2 + (-13 * -1 + -12x * -1 + x2 * -1) = 13 -6x + 3x2 + (13 + 12x + -1x2) = 13 Reorder the terms: 13 + -6x + 12x + 3x2 + -1x2 = 13 Combine like terms: -6x + 12x = 6x 13 + 6x + 3x2 + -1x2 = 13 Combine like terms: 3x2 + -1x2 = 2x2 13 + 6x + 2x2 = 13 Add '-13' to each side of the equation. 13 + 6x + -13 + 2x2 = 13 + -13 Reorder the terms: 13 + -13 + 6x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 0 + 6x + 2x2 = 13 + -13 6x + 2x2 = 13 + -13 Combine like terms: 13 + -13 = 0 6x + 2x2 = 0 Solving 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, -3}
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