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Simplifying 3x(4x + -5)(3x + -4) = 0 Reorder the terms: 3x(-5 + 4x)(3x + -4) = 0 Reorder the terms: 3x(-5 + 4x)(-4 + 3x) = 0 Multiply (-5 + 4x) * (-4 + 3x) 3x(-5(-4 + 3x) + 4x * (-4 + 3x)) = 0 3x((-4 * -5 + 3x * -5) + 4x * (-4 + 3x)) = 0 3x((20 + -15x) + 4x * (-4 + 3x)) = 0 3x(20 + -15x + (-4 * 4x + 3x * 4x)) = 0 3x(20 + -15x + (-16x + 12x2)) = 0 Combine like terms: -15x + -16x = -31x 3x(20 + -31x + 12x2) = 0 (20 * 3x + -31x * 3x + 12x2 * 3x) = 0 (60x + -93x2 + 36x3) = 0 Solving 60x + -93x2 + 36x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x'. 3x(20 + -31x + 12x2) = 0 Factor a trinomial. 3x((5 + -4x)(4 + -3x)) = 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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Subproblem 3
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 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 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0, 1.25, 1.333333333}
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