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Simplifying 3(x + -4)(2x + 1) = 0 Reorder the terms: 3(-4 + x)(2x + 1) = 0 Reorder the terms: 3(-4 + x)(1 + 2x) = 0 Multiply (-4 + x) * (1 + 2x) 3(-4(1 + 2x) + x(1 + 2x)) = 0 3((1 * -4 + 2x * -4) + x(1 + 2x)) = 0 3((-4 + -8x) + x(1 + 2x)) = 0 3(-4 + -8x + (1 * x + 2x * x)) = 0 3(-4 + -8x + (1x + 2x2)) = 0 Combine like terms: -8x + 1x = -7x 3(-4 + -7x + 2x2) = 0 (-4 * 3 + -7x * 3 + 2x2 * 3) = 0 (-12 + -21x + 6x2) = 0 Solving -12 + -21x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + -7x + 2x2) = 0 Factor a trinomial. 3((-1 + -2x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 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 = {-0.5, 4}
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