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Simplifying 3(5 + -2x)(3 + 4x) = 0 Multiply (5 + -2x) * (3 + 4x) 3(5(3 + 4x) + -2x * (3 + 4x)) = 0 3((3 * 5 + 4x * 5) + -2x * (3 + 4x)) = 0 3((15 + 20x) + -2x * (3 + 4x)) = 0 3(15 + 20x + (3 * -2x + 4x * -2x)) = 0 3(15 + 20x + (-6x + -8x2)) = 0 Combine like terms: 20x + -6x = 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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