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Simplifying (x + -3)(5x + 2) + -2(x + -3)(x + 1) = 0 Reorder the terms: (-3 + x)(5x + 2) + -2(x + -3)(x + 1) = 0 Reorder the terms: (-3 + x)(2 + 5x) + -2(x + -3)(x + 1) = 0 Multiply (-3 + x) * (2 + 5x) (-3(2 + 5x) + x(2 + 5x)) + -2(x + -3)(x + 1) = 0 ((2 * -3 + 5x * -3) + x(2 + 5x)) + -2(x + -3)(x + 1) = 0 ((-6 + -15x) + x(2 + 5x)) + -2(x + -3)(x + 1) = 0 (-6 + -15x + (2 * x + 5x * x)) + -2(x + -3)(x + 1) = 0 (-6 + -15x + (2x + 5x2)) + -2(x + -3)(x + 1) = 0 Combine like terms: -15x + 2x = -13x (-6 + -13x + 5x2) + -2(x + -3)(x + 1) = 0 Reorder the terms: -6 + -13x + 5x2 + -2(-3 + x)(x + 1) = 0 Reorder the terms: -6 + -13x + 5x2 + -2(-3 + x)(1 + x) = 0 Multiply (-3 + x) * (1 + x) -6 + -13x + 5x2 + -2(-3(1 + x) + x(1 + x)) = 0 -6 + -13x + 5x2 + -2((1 * -3 + x * -3) + x(1 + x)) = 0 -6 + -13x + 5x2 + -2((-3 + -3x) + x(1 + x)) = 0 -6 + -13x + 5x2 + -2(-3 + -3x + (1 * x + x * x)) = 0 -6 + -13x + 5x2 + -2(-3 + -3x + (1x + x2)) = 0 Combine like terms: -3x + 1x = -2x -6 + -13x + 5x2 + -2(-3 + -2x + x2) = 0 -6 + -13x + 5x2 + (-3 * -2 + -2x * -2 + x2 * -2) = 0 -6 + -13x + 5x2 + (6 + 4x + -2x2) = 0 Reorder the terms: -6 + 6 + -13x + 4x + 5x2 + -2x2 = 0 Combine like terms: -6 + 6 = 0 0 + -13x + 4x + 5x2 + -2x2 = 0 -13x + 4x + 5x2 + -2x2 = 0 Combine like terms: -13x + 4x = -9x -9x + 5x2 + -2x2 = 0 Combine like terms: 5x2 + -2x2 = 3x2 -9x + 3x2 = 0 Solving -9x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-3 + x) = 0 Ignore the factor 3.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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