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Simplifying 2(x + 5)(3 + -4x) = 0 Reorder the terms: 2(5 + x)(3 + -4x) = 0 Multiply (5 + x) * (3 + -4x) 2(5(3 + -4x) + x(3 + -4x)) = 0 2((3 * 5 + -4x * 5) + x(3 + -4x)) = 0 2((15 + -20x) + x(3 + -4x)) = 0 2(15 + -20x + (3 * x + -4x * x)) = 0 2(15 + -20x + (3x + -4x2)) = 0 Combine like terms: -20x + 3x = -17x 2(15 + -17x + -4x2) = 0 (15 * 2 + -17x * 2 + -4x2 * 2) = 0 (30 + -34x + -8x2) = 0 Solving 30 + -34x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -17x + -4x2) = 0 Factor a trinomial. 2((3 + -4x)(5 + x)) = 0 Ignore the factor 2.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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0.75, -5}
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