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Simplifying 2(x + -4)(4x + 3) = 0 Reorder the terms: 2(-4 + x)(4x + 3) = 0 Reorder the terms: 2(-4 + x)(3 + 4x) = 0 Multiply (-4 + x) * (3 + 4x) 2(-4(3 + 4x) + x(3 + 4x)) = 0 2((3 * -4 + 4x * -4) + x(3 + 4x)) = 0 2((-12 + -16x) + x(3 + 4x)) = 0 2(-12 + -16x + (3 * x + 4x * x)) = 0 2(-12 + -16x + (3x + 4x2)) = 0 Combine like terms: -16x + 3x = -13x 2(-12 + -13x + 4x2) = 0 (-12 * 2 + -13x * 2 + 4x2 * 2) = 0 (-24 + -26x + 8x2) = 0 Solving -24 + -26x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -13x + 4x2) = 0 Factor a trinomial. 2((-3 + -4x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.75Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-0.75, 4}
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