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Simplifying 4x(1 + 5x)(x + 3) = 0 Reorder the terms: 4x(1 + 5x)(3 + x) = 0 Multiply (1 + 5x) * (3 + x) 4x(1(3 + x) + 5x * (3 + x)) = 0 4x((3 * 1 + x * 1) + 5x * (3 + x)) = 0 4x((3 + 1x) + 5x * (3 + x)) = 0 4x(3 + 1x + (3 * 5x + x * 5x)) = 0 4x(3 + 1x + (15x + 5x2)) = 0 Combine like terms: 1x + 15x = 16x 4x(3 + 16x + 5x2) = 0 (3 * 4x + 16x * 4x + 5x2 * 4x) = 0 (12x + 64x2 + 20x3) = 0 Solving 12x + 64x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3 + 16x + 5x2) = 0 Factor a trinomial. 4x((3 + x)(1 + 5x)) = 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 + 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 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2Solution
x = {0, -3, -0.2}
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