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Simplifying (3 + -2x)(4x + 8) = 0 Reorder the terms: (3 + -2x)(8 + 4x) = 0 Multiply (3 + -2x) * (8 + 4x) (3(8 + 4x) + -2x * (8 + 4x)) = 0 ((8 * 3 + 4x * 3) + -2x * (8 + 4x)) = 0 ((24 + 12x) + -2x * (8 + 4x)) = 0 (24 + 12x + (8 * -2x + 4x * -2x)) = 0 (24 + 12x + (-16x + -8x2)) = 0 Combine like terms: 12x + -16x = -4x (24 + -4x + -8x2) = 0 Solving 24 + -4x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -1x + -2x2) = 0 Factor a trinomial. 4((3 + -2x)(2 + x)) = 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {1.5, -2}
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