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Simplifying (-2x + 3)(3x + -3) = 0 Reorder the terms: (3 + -2x)(3x + -3) = 0 Reorder the terms: (3 + -2x)(-3 + 3x) = 0 Multiply (3 + -2x) * (-3 + 3x) (3(-3 + 3x) + -2x * (-3 + 3x)) = 0 ((-3 * 3 + 3x * 3) + -2x * (-3 + 3x)) = 0 ((-9 + 9x) + -2x * (-3 + 3x)) = 0 (-9 + 9x + (-3 * -2x + 3x * -2x)) = 0 (-9 + 9x + (6x + -6x2)) = 0 Combine like terms: 9x + 6x = 15x (-9 + 15x + -6x2) = 0 Solving -9 + 15x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 5x + -2x2) = 0 Factor a trinomial. 3((-3 + 2x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = 1.5Subproblem 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 = {1.5, 1}
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