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Simplifying (3x + 1)(2x + -1) = 11x + -7 Reorder the terms: (1 + 3x)(2x + -1) = 11x + -7 Reorder the terms: (1 + 3x)(-1 + 2x) = 11x + -7 Multiply (1 + 3x) * (-1 + 2x) (1(-1 + 2x) + 3x * (-1 + 2x)) = 11x + -7 ((-1 * 1 + 2x * 1) + 3x * (-1 + 2x)) = 11x + -7 ((-1 + 2x) + 3x * (-1 + 2x)) = 11x + -7 (-1 + 2x + (-1 * 3x + 2x * 3x)) = 11x + -7 (-1 + 2x + (-3x + 6x2)) = 11x + -7 Combine like terms: 2x + -3x = -1x (-1 + -1x + 6x2) = 11x + -7 Reorder the terms: -1 + -1x + 6x2 = -7 + 11x Solving -1 + -1x + 6x2 = -7 + 11x Solving for variable 'x'. Reorder the terms: -1 + 7 + -1x + -11x + 6x2 = -7 + 11x + 7 + -11x Combine like terms: -1 + 7 = 6 6 + -1x + -11x + 6x2 = -7 + 11x + 7 + -11x Combine like terms: -1x + -11x = -12x 6 + -12x + 6x2 = -7 + 11x + 7 + -11x Reorder the terms: 6 + -12x + 6x2 = -7 + 7 + 11x + -11x Combine like terms: -7 + 7 = 0 6 + -12x + 6x2 = 0 + 11x + -11x 6 + -12x + 6x2 = 11x + -11x Combine like terms: 11x + -11x = 0 6 + -12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(1 + -2x + x2) = 0 Factor a trinomial. 6((1 + -1x)(1 + -1x)) = 0 Ignore the factor 6.Subproblem 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 '(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 = 1Solution
x = {1, 1}
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