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Simplifying (2x + -3)(6 + -2x) = 0 Reorder the terms: (-3 + 2x)(6 + -2x) = 0 Multiply (-3 + 2x) * (6 + -2x) (-3(6 + -2x) + 2x * (6 + -2x)) = 0 ((6 * -3 + -2x * -3) + 2x * (6 + -2x)) = 0 ((-18 + 6x) + 2x * (6 + -2x)) = 0 (-18 + 6x + (6 * 2x + -2x * 2x)) = 0 (-18 + 6x + (12x + -4x2)) = 0 Combine like terms: 6x + 12x = 18x (-18 + 18x + -4x2) = 0 Solving -18 + 18x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 9x + -2x2) = 0 Factor a trinomial. 2((-3 + x)(3 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 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 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 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 = {3, 1.5}
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