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Simplifying 15x(x + -1) = -3(5 + -1x) + 12x Reorder the terms: 15x(-1 + x) = -3(5 + -1x) + 12x (-1 * 15x + x * 15x) = -3(5 + -1x) + 12x (-15x + 15x2) = -3(5 + -1x) + 12x -15x + 15x2 = (5 * -3 + -1x * -3) + 12x -15x + 15x2 = (-15 + 3x) + 12x Combine like terms: 3x + 12x = 15x -15x + 15x2 = -15 + 15x Solving -15x + 15x2 = -15 + 15x Solving for variable 'x'. Reorder the terms: 15 + -15x + -15x + 15x2 = -15 + 15x + 15 + -15x Combine like terms: -15x + -15x = -30x 15 + -30x + 15x2 = -15 + 15x + 15 + -15x Reorder the terms: 15 + -30x + 15x2 = -15 + 15 + 15x + -15x Combine like terms: -15 + 15 = 0 15 + -30x + 15x2 = 0 + 15x + -15x 15 + -30x + 15x2 = 15x + -15x Combine like terms: 15x + -15x = 0 15 + -30x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(1 + -2x + x2) = 0 Factor a trinomial. 15((1 + -1x)(1 + -1x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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