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Simplifying 3(4x + -3)(2x + 5) = 0 Reorder the terms: 3(-3 + 4x)(2x + 5) = 0 Reorder the terms: 3(-3 + 4x)(5 + 2x) = 0 Multiply (-3 + 4x) * (5 + 2x) 3(-3(5 + 2x) + 4x * (5 + 2x)) = 0 3((5 * -3 + 2x * -3) + 4x * (5 + 2x)) = 0 3((-15 + -6x) + 4x * (5 + 2x)) = 0 3(-15 + -6x + (5 * 4x + 2x * 4x)) = 0 3(-15 + -6x + (20x + 8x2)) = 0 Combine like terms: -6x + 20x = 14x 3(-15 + 14x + 8x2) = 0 (-15 * 3 + 14x * 3 + 8x2 * 3) = 0 (-45 + 42x + 24x2) = 0 Solving -45 + 42x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 14x + 8x2) = 0 Factor a trinomial. 3((-5 + -2x)(3 + -4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
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 = 0.75Solution
x = {-2.5, 0.75}
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