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Simplifying 6x + 2x(x + 7) = 48 Reorder the terms: 6x + 2x(7 + x) = 48 6x + (7 * 2x + x * 2x) = 48 6x + (14x + 2x2) = 48 Combine like terms: 6x + 14x = 20x 20x + 2x2 = 48 Solving 20x + 2x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + 20x + 2x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 10x + x2) = 0 Factor a trinomial. 2((-12 + -1x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 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 = {-12, 2}
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