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Simplifying 6x(x + -1) = 1 + -7x Reorder the terms: 6x(-1 + x) = 1 + -7x (-1 * 6x + x * 6x) = 1 + -7x (-6x + 6x2) = 1 + -7x Solving -6x + 6x2 = 1 + -7x Solving for variable 'x'. Reorder the terms: -1 + -6x + 7x + 6x2 = 1 + -7x + -1 + 7x Combine like terms: -6x + 7x = 1x -1 + 1x + 6x2 = 1 + -7x + -1 + 7x Reorder the terms: -1 + 1x + 6x2 = 1 + -1 + -7x + 7x Combine like terms: 1 + -1 = 0 -1 + 1x + 6x2 = 0 + -7x + 7x -1 + 1x + 6x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -1 + 1x + 6x2 = 0 Factor a trinomial. (-1 + -2x)(1 + -3x) = 0Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 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 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-0.5, 0.3333333333}
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