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Simplifying 2x(x + -1) + 7x(x + -1) = 0 Reorder the terms: 2x(-1 + x) + 7x(x + -1) = 0 (-1 * 2x + x * 2x) + 7x(x + -1) = 0 (-2x + 2x2) + 7x(x + -1) = 0 Reorder the terms: -2x + 2x2 + 7x(-1 + x) = 0 -2x + 2x2 + (-1 * 7x + x * 7x) = 0 -2x + 2x2 + (-7x + 7x2) = 0 Reorder the terms: -2x + -7x + 2x2 + 7x2 = 0 Combine like terms: -2x + -7x = -9x -9x + 2x2 + 7x2 = 0 Combine like terms: 2x2 + 7x2 = 9x2 -9x + 9x2 = 0 Solving -9x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9x'. 9x(-1 + x) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
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 = 1Solution
x = {0, 1}
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