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Simplifying 2x(3x + 5)(6x + -8) = 0 Reorder the terms: 2x(5 + 3x)(6x + -8) = 0 Reorder the terms: 2x(5 + 3x)(-8 + 6x) = 0 Multiply (5 + 3x) * (-8 + 6x) 2x(5(-8 + 6x) + 3x * (-8 + 6x)) = 0 2x((-8 * 5 + 6x * 5) + 3x * (-8 + 6x)) = 0 2x((-40 + 30x) + 3x * (-8 + 6x)) = 0 2x(-40 + 30x + (-8 * 3x + 6x * 3x)) = 0 2x(-40 + 30x + (-24x + 18x2)) = 0 Combine like terms: 30x + -24x = 6x 2x(-40 + 6x + 18x2) = 0 (-40 * 2x + 6x * 2x + 18x2 * 2x) = 0 (-80x + 12x2 + 36x3) = 0 Solving -80x + 12x2 + 36x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-20 + 3x + 9x2) = 0 Factor a trinomial. 4x((-5 + -3x)(4 + -3x)) = 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 '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 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, -1.666666667, 1.333333333}
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