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Simplifying 5x(x + -3) = (2x + 3)(x + -3) Reorder the terms: 5x(-3 + x) = (2x + 3)(x + -3) (-3 * 5x + x * 5x) = (2x + 3)(x + -3) (-15x + 5x2) = (2x + 3)(x + -3) Reorder the terms: -15x + 5x2 = (3 + 2x)(x + -3) Reorder the terms: -15x + 5x2 = (3 + 2x)(-3 + x) Multiply (3 + 2x) * (-3 + x) -15x + 5x2 = (3(-3 + x) + 2x * (-3 + x)) -15x + 5x2 = ((-3 * 3 + x * 3) + 2x * (-3 + x)) -15x + 5x2 = ((-9 + 3x) + 2x * (-3 + x)) -15x + 5x2 = (-9 + 3x + (-3 * 2x + x * 2x)) -15x + 5x2 = (-9 + 3x + (-6x + 2x2)) Combine like terms: 3x + -6x = -3x -15x + 5x2 = (-9 + -3x + 2x2) Solving -15x + 5x2 = -9 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: 9 + -15x + 3x + 5x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Combine like terms: -15x + 3x = -12x 9 + -12x + 5x2 + -2x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 9 + -12x + 3x2 = -9 + -3x + 2x2 + 9 + 3x + -2x2 Reorder the terms: 9 + -12x + 3x2 = -9 + 9 + -3x + 3x + 2x2 + -2x2 Combine like terms: -9 + 9 = 0 9 + -12x + 3x2 = 0 + -3x + 3x + 2x2 + -2x2 9 + -12x + 3x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 9 + -12x + 3x2 = 0 + 2x2 + -2x2 9 + -12x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + -12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -4x + x2) = 0 Factor a trinomial. 3((1 + -1x)(3 + -1x)) = 0 Ignore the factor 3.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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {1, 3}
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