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Simplifying (2x + 3)(12x + -3) = 0 Reorder the terms: (3 + 2x)(12x + -3) = 0 Reorder the terms: (3 + 2x)(-3 + 12x) = 0 Multiply (3 + 2x) * (-3 + 12x) (3(-3 + 12x) + 2x * (-3 + 12x)) = 0 ((-3 * 3 + 12x * 3) + 2x * (-3 + 12x)) = 0 ((-9 + 36x) + 2x * (-3 + 12x)) = 0 (-9 + 36x + (-3 * 2x + 12x * 2x)) = 0 (-9 + 36x + (-6x + 24x2)) = 0 Combine like terms: 36x + -6x = 30x (-9 + 30x + 24x2) = 0 Solving -9 + 30x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 10x + 8x2) = 0 Factor a trinomial. 3((-3 + -2x)(1 + -4x)) = 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-1.5, 0.25}
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