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