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Simplifying (2x + -5)(9x + -15) = 0 Reorder the terms: (-5 + 2x)(9x + -15) = 0 Reorder the terms: (-5 + 2x)(-15 + 9x) = 0 Multiply (-5 + 2x) * (-15 + 9x) (-5(-15 + 9x) + 2x * (-15 + 9x)) = 0 ((-15 * -5 + 9x * -5) + 2x * (-15 + 9x)) = 0 ((75 + -45x) + 2x * (-15 + 9x)) = 0 (75 + -45x + (-15 * 2x + 9x * 2x)) = 0 (75 + -45x + (-30x + 18x2)) = 0 Combine like terms: -45x + -30x = -75x (75 + -75x + 18x2) = 0 Solving 75 + -75x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -25x + 6x2) = 0 Factor a trinomial. 3((5 + -3x)(5 + -2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 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 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Subproblem 2
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 = 2.5Solution
x = {1.666666667, 2.5}
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