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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((1 + -1x)(3 + -2x)) = 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 + -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 = {1, 1.5}
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