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Simplifying (8x + 3) * x(4x + 27) = 0 Reorder the terms: (3 + 8x) * x(4x + 27) = 0 Reorder the terms: (3 + 8x) * x(27 + 4x) = 0 Reorder the terms for easier multiplication: x(3 + 8x)(27 + 4x) = 0 Multiply (3 + 8x) * (27 + 4x) x(3(27 + 4x) + 8x * (27 + 4x)) = 0 x((27 * 3 + 4x * 3) + 8x * (27 + 4x)) = 0 x((81 + 12x) + 8x * (27 + 4x)) = 0 x(81 + 12x + (27 * 8x + 4x * 8x)) = 0 x(81 + 12x + (216x + 32x2)) = 0 Combine like terms: 12x + 216x = 228x x(81 + 228x + 32x2) = 0 (81 * x + 228x * x + 32x2 * x) = 0 (81x + 228x2 + 32x3) = 0 Solving 81x + 228x2 + 32x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(81 + 228x + 32x2) = 0 Factor a trinomial. x((27 + 4x)(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 '(27 + 4x)' equal to zero and attempt to solve: Simplifying 27 + 4x = 0 Solving 27 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 4x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 4x = 0 + -27 4x = 0 + -27 Combine like terms: 0 + -27 = -27 4x = -27 Divide each side by '4'. x = -6.75 Simplifying x = -6.75Subproblem 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, -6.75, -0.375}
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