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Simplifying (8x + 3)(5x + -15) = 0 Reorder the terms: (3 + 8x)(5x + -15) = 0 Reorder the terms: (3 + 8x)(-15 + 5x) = 0 Multiply (3 + 8x) * (-15 + 5x) (3(-15 + 5x) + 8x * (-15 + 5x)) = 0 ((-15 * 3 + 5x * 3) + 8x * (-15 + 5x)) = 0 ((-45 + 15x) + 8x * (-15 + 5x)) = 0 (-45 + 15x + (-15 * 8x + 5x * 8x)) = 0 (-45 + 15x + (-120x + 40x2)) = 0 Combine like terms: 15x + -120x = -105x (-45 + -105x + 40x2) = 0 Solving -45 + -105x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -21x + 8x2) = 0 Factor a trinomial. 5((-3 + -8x)(3 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -8x)' equal to zero and attempt to solve: Simplifying -3 + -8x = 0 Solving -3 + -8x = 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 + -8x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x = 0 + 3 -8x = 0 + 3 Combine like terms: 0 + 3 = 3 -8x = 3 Divide each side by '-8'. x = -0.375 Simplifying x = -0.375Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-0.375, 3}
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