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Simplifying -3x2 + 30x + -75 = -27 Reorder the terms: -75 + 30x + -3x2 = -27 Solving -75 + 30x + -3x2 = -27 Solving for variable 'x'. Reorder the terms: -75 + 27 + 30x + -3x2 = -27 + 27 Combine like terms: -75 + 27 = -48 -48 + 30x + -3x2 = -27 + 27 Combine like terms: -27 + 27 = 0 -48 + 30x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-16 + 10x + -1x2) = 0 Factor a trinomial. 3((-8 + x)(2 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {8, 2}
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