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Simplifying 6x(x + 1) + -7x = 7 Reorder the terms: 6x(1 + x) + -7x = 7 (1 * 6x + x * 6x) + -7x = 7 (6x + 6x2) + -7x = 7 Reorder the terms: 6x + -7x + 6x2 = 7 Combine like terms: 6x + -7x = -1x -1x + 6x2 = 7 Solving -1x + 6x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + -1x + 6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -1x + 6x2 = 0 Factor a trinomial. (-1 + -1x)(7 + -6x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Divide each side by '-6'. x = 1.166666667 Simplifying x = 1.166666667Solution
x = {-1, 1.166666667}
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