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Simplifying (4x + 9)(5x + -5) = 0 Reorder the terms: (9 + 4x)(5x + -5) = 0 Reorder the terms: (9 + 4x)(-5 + 5x) = 0 Multiply (9 + 4x) * (-5 + 5x) (9(-5 + 5x) + 4x * (-5 + 5x)) = 0 ((-5 * 9 + 5x * 9) + 4x * (-5 + 5x)) = 0 ((-45 + 45x) + 4x * (-5 + 5x)) = 0 (-45 + 45x + (-5 * 4x + 5x * 4x)) = 0 (-45 + 45x + (-20x + 20x2)) = 0 Combine like terms: 45x + -20x = 25x (-45 + 25x + 20x2) = 0 Solving -45 + 25x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + 5x + 4x2) = 0 Factor a trinomial. 5((-9 + -4x)(1 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve: Simplifying -9 + -4x = 0 Solving -9 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x = 0 + 9 -4x = 0 + 9 Combine like terms: 0 + 9 = 9 -4x = 9 Divide each side by '-4'. x = -2.25 Simplifying x = -2.25Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-2.25, 1}
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