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Simplifying 6x2 = 45x + -75 Reorder the terms: 6x2 = -75 + 45x Solving 6x2 = -75 + 45x Solving for variable 'x'. Reorder the terms: 75 + -45x + 6x2 = -75 + 45x + 75 + -45x Reorder the terms: 75 + -45x + 6x2 = -75 + 75 + 45x + -45x Combine like terms: -75 + 75 = 0 75 + -45x + 6x2 = 0 + 45x + -45x 75 + -45x + 6x2 = 45x + -45x Combine like terms: 45x + -45x = 0 75 + -45x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -15x + 2x2) = 0 Factor a trinomial. 3((5 + -2x)(5 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Subproblem 2
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 = 5Solution
x = {2.5, 5}
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