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Simplifying 3x + 15 + 3x2 = 75 Reorder the terms: 15 + 3x + 3x2 = 75 Solving 15 + 3x + 3x2 = 75 Solving for variable 'x'. Reorder the terms: 15 + -75 + 3x + 3x2 = 75 + -75 Combine like terms: 15 + -75 = -60 -60 + 3x + 3x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -60 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + x + x2) = 0 Factor a trinomial. 3((-5 + -1x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-5, 4}
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