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Simplifying 4x((3 + 2x)(1 + x)) = 0 Multiply (3 + 2x) * (1 + x) 4x((3(1 + x) + 2x * (1 + x))) = 0 4x(((1 * 3 + x * 3) + 2x * (1 + x))) = 0 4x(((3 + 3x) + 2x * (1 + x))) = 0 4x((3 + 3x + (1 * 2x + x * 2x))) = 0 4x((3 + 3x + (2x + 2x2))) = 0 Combine like terms: 3x + 2x = 5x 4x((3 + 5x + 2x2)) = 0 (3 * 4x + 5x * 4x + 2x2 * 4x) = 0 (12x + 20x2 + 8x3) = 0 Solving 12x + 20x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + 5x + 2x2) = 0 Factor a trinomial. 4x((3 + 2x)(1 + x)) = 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 '(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 3
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 = -1Solution
x = {0, -1.5, -1}
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