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Simplifying (2x + 1)(8x2 + 3x) = 0 Reorder the terms: (1 + 2x)(8x2 + 3x) = 0 Reorder the terms: (1 + 2x)(3x + 8x2) = 0 Multiply (1 + 2x) * (3x + 8x2) (1(3x + 8x2) + 2x * (3x + 8x2)) = 0 ((3x * 1 + 8x2 * 1) + 2x * (3x + 8x2)) = 0 ((3x + 8x2) + 2x * (3x + 8x2)) = 0 (3x + 8x2 + (3x * 2x + 8x2 * 2x)) = 0 (3x + 8x2 + (6x2 + 16x3)) = 0 Combine like terms: 8x2 + 6x2 = 14x2 (3x + 14x2 + 16x3) = 0 Solving 3x + 14x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 14x + 16x2) = 0 Factor a trinomial. x((1 + 2x)(3 + 8x)) = 0Subproblem 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 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 3
Set the factor '(3 + 8x)' equal to zero and attempt to solve: Simplifying 3 + 8x = 0 Solving 3 + 8x = 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 + 8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 8x = 0 + -3 8x = 0 + -3 Combine like terms: 0 + -3 = -3 8x = -3 Divide each side by '8'. x = -0.375 Simplifying x = -0.375Solution
x = {0, -0.5, -0.375}
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