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Simplifying (x + -5)(-3x + 9) = 0 Reorder the terms: (-5 + x)(-3x + 9) = 0 Reorder the terms: (-5 + x)(9 + -3x) = 0 Multiply (-5 + x) * (9 + -3x) (-5(9 + -3x) + x(9 + -3x)) = 0 ((9 * -5 + -3x * -5) + x(9 + -3x)) = 0 ((-45 + 15x) + x(9 + -3x)) = 0 (-45 + 15x + (9 * x + -3x * x)) = 0 (-45 + 15x + (9x + -3x2)) = 0 Combine like terms: 15x + 9x = 24x (-45 + 24x + -3x2) = 0 Solving -45 + 24x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 8x + -1x2) = 0 Factor a trinomial. 3((-5 + x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = 5Subproblem 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 = {5, 3}
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