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Simplifying (4x + -16)(2x + 3) = 0 Reorder the terms: (-16 + 4x)(2x + 3) = 0 Reorder the terms: (-16 + 4x)(3 + 2x) = 0 Multiply (-16 + 4x) * (3 + 2x) (-16(3 + 2x) + 4x * (3 + 2x)) = 0 ((3 * -16 + 2x * -16) + 4x * (3 + 2x)) = 0 ((-48 + -32x) + 4x * (3 + 2x)) = 0 (-48 + -32x + (3 * 4x + 2x * 4x)) = 0 (-48 + -32x + (12x + 8x2)) = 0 Combine like terms: -32x + 12x = -20x (-48 + -20x + 8x2) = 0 Solving -48 + -20x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -5x + 2x2) = 0 Factor a trinomial. 4((-3 + -2x)(4 + -1x)) = 0 Ignore the factor 4.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 '(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 = {-1.5, 4}
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