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Simplifying (9x + 7)(2x + -3) = (6x + -5)(2x + -3) Reorder the terms: (7 + 9x)(2x + -3) = (6x + -5)(2x + -3) Reorder the terms: (7 + 9x)(-3 + 2x) = (6x + -5)(2x + -3) Multiply (7 + 9x) * (-3 + 2x) (7(-3 + 2x) + 9x * (-3 + 2x)) = (6x + -5)(2x + -3) ((-3 * 7 + 2x * 7) + 9x * (-3 + 2x)) = (6x + -5)(2x + -3) ((-21 + 14x) + 9x * (-3 + 2x)) = (6x + -5)(2x + -3) (-21 + 14x + (-3 * 9x + 2x * 9x)) = (6x + -5)(2x + -3) (-21 + 14x + (-27x + 18x2)) = (6x + -5)(2x + -3) Combine like terms: 14x + -27x = -13x (-21 + -13x + 18x2) = (6x + -5)(2x + -3) Reorder the terms: -21 + -13x + 18x2 = (-5 + 6x)(2x + -3) Reorder the terms: -21 + -13x + 18x2 = (-5 + 6x)(-3 + 2x) Multiply (-5 + 6x) * (-3 + 2x) -21 + -13x + 18x2 = (-5(-3 + 2x) + 6x * (-3 + 2x)) -21 + -13x + 18x2 = ((-3 * -5 + 2x * -5) + 6x * (-3 + 2x)) -21 + -13x + 18x2 = ((15 + -10x) + 6x * (-3 + 2x)) -21 + -13x + 18x2 = (15 + -10x + (-3 * 6x + 2x * 6x)) -21 + -13x + 18x2 = (15 + -10x + (-18x + 12x2)) Combine like terms: -10x + -18x = -28x -21 + -13x + 18x2 = (15 + -28x + 12x2) Solving -21 + -13x + 18x2 = 15 + -28x + 12x2 Solving for variable 'x'. Reorder the terms: -21 + -15 + -13x + 28x + 18x2 + -12x2 = 15 + -28x + 12x2 + -15 + 28x + -12x2 Combine like terms: -21 + -15 = -36 -36 + -13x + 28x + 18x2 + -12x2 = 15 + -28x + 12x2 + -15 + 28x + -12x2 Combine like terms: -13x + 28x = 15x -36 + 15x + 18x2 + -12x2 = 15 + -28x + 12x2 + -15 + 28x + -12x2 Combine like terms: 18x2 + -12x2 = 6x2 -36 + 15x + 6x2 = 15 + -28x + 12x2 + -15 + 28x + -12x2 Reorder the terms: -36 + 15x + 6x2 = 15 + -15 + -28x + 28x + 12x2 + -12x2 Combine like terms: 15 + -15 = 0 -36 + 15x + 6x2 = 0 + -28x + 28x + 12x2 + -12x2 -36 + 15x + 6x2 = -28x + 28x + 12x2 + -12x2 Combine like terms: -28x + 28x = 0 -36 + 15x + 6x2 = 0 + 12x2 + -12x2 -36 + 15x + 6x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -36 + 15x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 5x + 2x2) = 0 Factor a trinomial. 3((-4 + -1x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-4, 1.5}
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