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Simplifying 7x(x + 6) = 2x + 12 Reorder the terms: 7x(6 + x) = 2x + 12 (6 * 7x + x * 7x) = 2x + 12 (42x + 7x2) = 2x + 12 Reorder the terms: 42x + 7x2 = 12 + 2x Solving 42x + 7x2 = 12 + 2x Solving for variable 'x'. Reorder the terms: -12 + 42x + -2x + 7x2 = 12 + 2x + -12 + -2x Combine like terms: 42x + -2x = 40x -12 + 40x + 7x2 = 12 + 2x + -12 + -2x Reorder the terms: -12 + 40x + 7x2 = 12 + -12 + 2x + -2x Combine like terms: 12 + -12 = 0 -12 + 40x + 7x2 = 0 + 2x + -2x -12 + 40x + 7x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -12 + 40x + 7x2 = 0 Factor a trinomial. (-6 + -1x)(2 + -7x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {-6, 0.2857142857}
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