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Simplifying (2x + 4) * 2x(2x + 3) = 0 Reorder the terms: (4 + 2x) * 2x(2x + 3) = 0 Reorder the terms: (4 + 2x) * 2x(3 + 2x) = 0 Reorder the terms for easier multiplication: 2x(4 + 2x)(3 + 2x) = 0 Multiply (4 + 2x) * (3 + 2x) 2x(4(3 + 2x) + 2x * (3 + 2x)) = 0 2x((3 * 4 + 2x * 4) + 2x * (3 + 2x)) = 0 2x((12 + 8x) + 2x * (3 + 2x)) = 0 2x(12 + 8x + (3 * 2x + 2x * 2x)) = 0 2x(12 + 8x + (6x + 4x2)) = 0 Combine like terms: 8x + 6x = 14x 2x(12 + 14x + 4x2) = 0 (12 * 2x + 14x * 2x + 4x2 * 2x) = 0 (24x + 28x2 + 8x3) = 0 Solving 24x + 28x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(6 + 7x + 2x2) = 0 Factor a trinomial. 4x((2 + x)(3 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = -2Subproblem 3
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 = -1.5Solution
x = {0, -2, -1.5}
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