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Simplifying (x + 1)(x + -7) = (2x + 1)(x + -7) Reorder the terms: (1 + x)(x + -7) = (2x + 1)(x + -7) Reorder the terms: (1 + x)(-7 + x) = (2x + 1)(x + -7) Multiply (1 + x) * (-7 + x) (1(-7 + x) + x(-7 + x)) = (2x + 1)(x + -7) ((-7 * 1 + x * 1) + x(-7 + x)) = (2x + 1)(x + -7) ((-7 + 1x) + x(-7 + x)) = (2x + 1)(x + -7) (-7 + 1x + (-7 * x + x * x)) = (2x + 1)(x + -7) (-7 + 1x + (-7x + x2)) = (2x + 1)(x + -7) Combine like terms: 1x + -7x = -6x (-7 + -6x + x2) = (2x + 1)(x + -7) Reorder the terms: -7 + -6x + x2 = (1 + 2x)(x + -7) Reorder the terms: -7 + -6x + x2 = (1 + 2x)(-7 + x) Multiply (1 + 2x) * (-7 + x) -7 + -6x + x2 = (1(-7 + x) + 2x * (-7 + x)) -7 + -6x + x2 = ((-7 * 1 + x * 1) + 2x * (-7 + x)) -7 + -6x + x2 = ((-7 + 1x) + 2x * (-7 + x)) -7 + -6x + x2 = (-7 + 1x + (-7 * 2x + x * 2x)) -7 + -6x + x2 = (-7 + 1x + (-14x + 2x2)) Combine like terms: 1x + -14x = -13x -7 + -6x + x2 = (-7 + -13x + 2x2) Add '7' to each side of the equation. -7 + -6x + 7 + x2 = -7 + -13x + 7 + 2x2 Reorder the terms: -7 + 7 + -6x + x2 = -7 + -13x + 7 + 2x2 Combine like terms: -7 + 7 = 0 0 + -6x + x2 = -7 + -13x + 7 + 2x2 -6x + x2 = -7 + -13x + 7 + 2x2 Reorder the terms: -6x + x2 = -7 + 7 + -13x + 2x2 Combine like terms: -7 + 7 = 0 -6x + x2 = 0 + -13x + 2x2 -6x + x2 = -13x + 2x2 Solving -6x + x2 = -13x + 2x2 Solving for variable 'x'. Reorder the terms: -6x + 13x + x2 + -2x2 = -13x + 2x2 + 13x + -2x2 Combine like terms: -6x + 13x = 7x 7x + x2 + -2x2 = -13x + 2x2 + 13x + -2x2 Combine like terms: x2 + -2x2 = -1x2 7x + -1x2 = -13x + 2x2 + 13x + -2x2 Reorder the terms: 7x + -1x2 = -13x + 13x + 2x2 + -2x2 Combine like terms: -13x + 13x = 0 7x + -1x2 = 0 + 2x2 + -2x2 7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(7 + -1x) = 0Subproblem 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, 7}
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