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Simplifying 7 + 2(x + -6) = -3 + 2x(x + -1) Reorder the terms: 7 + 2(-6 + x) = -3 + 2x(x + -1) 7 + (-6 * 2 + x * 2) = -3 + 2x(x + -1) 7 + (-12 + 2x) = -3 + 2x(x + -1) Combine like terms: 7 + -12 = -5 -5 + 2x = -3 + 2x(x + -1) Reorder the terms: -5 + 2x = -3 + 2x(-1 + x) -5 + 2x = -3 + (-1 * 2x + x * 2x) -5 + 2x = -3 + (-2x + 2x2) Solving -5 + 2x = -3 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: -5 + 3 + 2x + 2x + -2x2 = -3 + -2x + 2x2 + 3 + 2x + -2x2 Combine like terms: -5 + 3 = -2 -2 + 2x + 2x + -2x2 = -3 + -2x + 2x2 + 3 + 2x + -2x2 Combine like terms: 2x + 2x = 4x -2 + 4x + -2x2 = -3 + -2x + 2x2 + 3 + 2x + -2x2 Reorder the terms: -2 + 4x + -2x2 = -3 + 3 + -2x + 2x + 2x2 + -2x2 Combine like terms: -3 + 3 = 0 -2 + 4x + -2x2 = 0 + -2x + 2x + 2x2 + -2x2 -2 + 4x + -2x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -2 + 4x + -2x2 = 0 + 2x2 + -2x2 -2 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + -1x2) = 0 Factor a trinomial. 2((-1 + x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 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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