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Simplifying (5x + -8)(3x + 9) = 0 Reorder the terms: (-8 + 5x)(3x + 9) = 0 Reorder the terms: (-8 + 5x)(9 + 3x) = 0 Multiply (-8 + 5x) * (9 + 3x) (-8(9 + 3x) + 5x * (9 + 3x)) = 0 ((9 * -8 + 3x * -8) + 5x * (9 + 3x)) = 0 ((-72 + -24x) + 5x * (9 + 3x)) = 0 (-72 + -24x + (9 * 5x + 3x * 5x)) = 0 (-72 + -24x + (45x + 15x2)) = 0 Combine like terms: -24x + 45x = 21x (-72 + 21x + 15x2) = 0 Solving -72 + 21x + 15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + 7x + 5x2) = 0 Factor a trinomial. 3((-3 + -1x)(8 + -5x)) = 0 Ignore the factor 3.Subproblem 1
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 = -3Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-3, 1.6}
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