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Simplifying (4x + 4) * x(4x + 3) = 0 Reorder the terms: (4 + 4x) * x(4x + 3) = 0 Reorder the terms: (4 + 4x) * x(3 + 4x) = 0 Reorder the terms for easier multiplication: x(4 + 4x)(3 + 4x) = 0 Multiply (4 + 4x) * (3 + 4x) x(4(3 + 4x) + 4x * (3 + 4x)) = 0 x((3 * 4 + 4x * 4) + 4x * (3 + 4x)) = 0 x((12 + 16x) + 4x * (3 + 4x)) = 0 x(12 + 16x + (3 * 4x + 4x * 4x)) = 0 x(12 + 16x + (12x + 16x2)) = 0 Combine like terms: 16x + 12x = 28x x(12 + 28x + 16x2) = 0 (12 * x + 28x * x + 16x2 * x) = 0 (12x + 28x2 + 16x3) = 0 Solving 12x + 28x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + 7x + 4x2) = 0 Factor a trinomial. 4x((1 + x)(3 + 4x)) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 3
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 = -0.75Solution
x = {0, -1, -0.75}
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