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Simplifying x(x + -1) = 2x + -3(3x + 3) + 2x(x + -1) Reorder the terms: x(-1 + x) = 2x + -3(3x + 3) + 2x(x + -1) (-1 * x + x * x) = 2x + -3(3x + 3) + 2x(x + -1) (-1x + x2) = 2x + -3(3x + 3) + 2x(x + -1) Reorder the terms: -1x + x2 = 2x + -3(3 + 3x) + 2x(x + -1) -1x + x2 = 2x + (3 * -3 + 3x * -3) + 2x(x + -1) -1x + x2 = 2x + (-9 + -9x) + 2x(x + -1) Reorder the terms: -1x + x2 = 2x + -9 + -9x + 2x(-1 + x) -1x + x2 = 2x + -9 + -9x + (-1 * 2x + x * 2x) -1x + x2 = 2x + -9 + -9x + (-2x + 2x2) Reorder the terms: -1x + x2 = -9 + 2x + -9x + -2x + 2x2 Combine like terms: 2x + -9x = -7x -1x + x2 = -9 + -7x + -2x + 2x2 Combine like terms: -7x + -2x = -9x -1x + x2 = -9 + -9x + 2x2 Solving -1x + x2 = -9 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: 9 + -1x + 9x + x2 + -2x2 = -9 + -9x + 2x2 + 9 + 9x + -2x2 Combine like terms: -1x + 9x = 8x 9 + 8x + x2 + -2x2 = -9 + -9x + 2x2 + 9 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 9 + 8x + -1x2 = -9 + -9x + 2x2 + 9 + 9x + -2x2 Reorder the terms: 9 + 8x + -1x2 = -9 + 9 + -9x + 9x + 2x2 + -2x2 Combine like terms: -9 + 9 = 0 9 + 8x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 9 + 8x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 9 + 8x + -1x2 = 0 + 2x2 + -2x2 9 + 8x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + 8x + -1x2 = 0 Factor a trinomial. (9 + -1x)(1 + x) = 0Subproblem 1
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Subproblem 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 = {9, -1}
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