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Simplifying (4x + 1)(x + 3)(x) = 0 Reorder the terms: (1 + 4x)(x + 3)(x) = 0 Reorder the terms: (1 + 4x)(3 + x)(x) = 0 Reorder the terms for easier multiplication: x(1 + 4x)(3 + x) = 0 Multiply (1 + 4x) * (3 + x) x(1(3 + x) + 4x * (3 + x)) = 0 x((3 * 1 + x * 1) + 4x * (3 + x)) = 0 x((3 + 1x) + 4x * (3 + x)) = 0 x(3 + 1x + (3 * 4x + x * 4x)) = 0 x(3 + 1x + (12x + 4x2)) = 0 Combine like terms: 1x + 12x = 13x x(3 + 13x + 4x2) = 0 (3 * x + 13x * x + 4x2 * x) = 0 (3x + 13x2 + 4x3) = 0 Solving 3x + 13x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 13x + 4x2) = 0 Factor a trinomial. x((3 + x)(1 + 4x)) = 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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {0, -3, -0.25}
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