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Simplifying (5x + 3)(2 + -8x) = 0 Reorder the terms: (3 + 5x)(2 + -8x) = 0 Multiply (3 + 5x) * (2 + -8x) (3(2 + -8x) + 5x * (2 + -8x)) = 0 ((2 * 3 + -8x * 3) + 5x * (2 + -8x)) = 0 ((6 + -24x) + 5x * (2 + -8x)) = 0 (6 + -24x + (2 * 5x + -8x * 5x)) = 0 (6 + -24x + (10x + -40x2)) = 0 Combine like terms: -24x + 10x = -14x (6 + -14x + -40x2) = 0 Solving 6 + -14x + -40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -7x + -20x2) = 0 Factor a trinomial. 2((1 + -4x)(3 + 5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Solution
x = {0.25, -0.6}
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