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Simplifying 3(6x + -5)(4x + 3) = 0 Reorder the terms: 3(-5 + 6x)(4x + 3) = 0 Reorder the terms: 3(-5 + 6x)(3 + 4x) = 0 Multiply (-5 + 6x) * (3 + 4x) 3(-5(3 + 4x) + 6x * (3 + 4x)) = 0 3((3 * -5 + 4x * -5) + 6x * (3 + 4x)) = 0 3((-15 + -20x) + 6x * (3 + 4x)) = 0 3(-15 + -20x + (3 * 6x + 4x * 6x)) = 0 3(-15 + -20x + (18x + 24x2)) = 0 Combine like terms: -20x + 18x = -2x 3(-15 + -2x + 24x2) = 0 (-15 * 3 + -2x * 3 + 24x2 * 3) = 0 (-45 + -6x + 72x2) = 0 Solving -45 + -6x + 72x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -2x + 24x2) = 0 Factor a trinomial. 3((-3 + -4x)(5 + -6x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve: Simplifying 5 + -6x = 0 Solving 5 + -6x = 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 + -6x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6x = 0 + -5 -6x = 0 + -5 Combine like terms: 0 + -5 = -5 -6x = -5 Divide each side by '-6'. x = 0.8333333333 Simplifying x = 0.8333333333Solution
x = {-0.75, 0.8333333333}
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