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Simplifying (4x + -3)(12x + 2) = 0 Reorder the terms: (-3 + 4x)(12x + 2) = 0 Reorder the terms: (-3 + 4x)(2 + 12x) = 0 Multiply (-3 + 4x) * (2 + 12x) (-3(2 + 12x) + 4x * (2 + 12x)) = 0 ((2 * -3 + 12x * -3) + 4x * (2 + 12x)) = 0 ((-6 + -36x) + 4x * (2 + 12x)) = 0 (-6 + -36x + (2 * 4x + 12x * 4x)) = 0 (-6 + -36x + (8x + 48x2)) = 0 Combine like terms: -36x + 8x = -28x (-6 + -28x + 48x2) = 0 Solving -6 + -28x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -14x + 24x2) = 0 Factor a trinomial. 2((-1 + -6x)(3 + -4x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve: Simplifying -1 + -6x = 0 Solving -1 + -6x = 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 + -6x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x = 0 + 1 -6x = 0 + 1 Combine like terms: 0 + 1 = 1 -6x = 1 Divide each side by '-6'. x = -0.1666666667 Simplifying x = -0.1666666667Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {-0.1666666667, 0.75}
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