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Simplifying 3x(2x + 1)(x + -8) = 0 Reorder the terms: 3x(1 + 2x)(x + -8) = 0 Reorder the terms: 3x(1 + 2x)(-8 + x) = 0 Multiply (1 + 2x) * (-8 + x) 3x(1(-8 + x) + 2x * (-8 + x)) = 0 3x((-8 * 1 + x * 1) + 2x * (-8 + x)) = 0 3x((-8 + 1x) + 2x * (-8 + x)) = 0 3x(-8 + 1x + (-8 * 2x + x * 2x)) = 0 3x(-8 + 1x + (-16x + 2x2)) = 0 Combine like terms: 1x + -16x = -15x 3x(-8 + -15x + 2x2) = 0 (-8 * 3x + -15x * 3x + 2x2 * 3x) = 0 (-24x + -45x2 + 6x3) = 0 Solving -24x + -45x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(-8 + -15x + 2x2) = 0 Factor a trinomial. 3x((-1 + -2x)(8 + -1x)) = 0 Ignore the factor 3.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 '(-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 '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {0, -0.5, 8}
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