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Simplifying 2x(4x + 3)(1x + 2) = 0 Reorder the terms: 2x(3 + 4x)(1x + 2) = 0 Reorder the terms: 2x(3 + 4x)(2 + 1x) = 0 Multiply (3 + 4x) * (2 + 1x) 2x(3(2 + 1x) + 4x * (2 + 1x)) = 0 2x((2 * 3 + 1x * 3) + 4x * (2 + 1x)) = 0 2x((6 + 3x) + 4x * (2 + 1x)) = 0 2x(6 + 3x + (2 * 4x + 1x * 4x)) = 0 2x(6 + 3x + (8x + 4x2)) = 0 Combine like terms: 3x + 8x = 11x 2x(6 + 11x + 4x2) = 0 (6 * 2x + 11x * 2x + 4x2 * 2x) = 0 (12x + 22x2 + 8x3) = 0 Solving 12x + 22x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + 11x + 4x2) = 0 Factor a trinomial. 2x((2 + x)(3 + 4x)) = 0 Ignore the factor 2.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 + 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, -2, -0.75}
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