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Simplifying x(-32 + -3x) = 45 (-32 * x + -3x * x) = 45 (-32x + -3x2) = 45 Solving -32x + -3x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -32x + -3x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -32x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 32x + 3x2) = 0 Factor a trinomial. -1((9 + x)(5 + 3x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 2
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 = -1.666666667Solution
x = {-9, -1.666666667}
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