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Simplifying 4x(5x + -6)(x + 4) = 0 Reorder the terms: 4x(-6 + 5x)(x + 4) = 0 Reorder the terms: 4x(-6 + 5x)(4 + x) = 0 Multiply (-6 + 5x) * (4 + x) 4x(-6(4 + x) + 5x * (4 + x)) = 0 4x((4 * -6 + x * -6) + 5x * (4 + x)) = 0 4x((-24 + -6x) + 5x * (4 + x)) = 0 4x(-24 + -6x + (4 * 5x + x * 5x)) = 0 4x(-24 + -6x + (20x + 5x2)) = 0 Combine like terms: -6x + 20x = 14x 4x(-24 + 14x + 5x2) = 0 (-24 * 4x + 14x * 4x + 5x2 * 4x) = 0 (-96x + 56x2 + 20x3) = 0 Solving -96x + 56x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-24 + 14x + 5x2) = 0 Factor a trinomial. 4x((-4 + -1x)(6 + -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 '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 3
Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {0, -4, 1.2}
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