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Simplifying 4x + -1(x + 5)(x + -7) = x(1 + -1x) Reorder the terms: 4x + -1(5 + x)(x + -7) = x(1 + -1x) Reorder the terms: 4x + -1(5 + x)(-7 + x) = x(1 + -1x) Multiply (5 + x) * (-7 + x) 4x + -1(5(-7 + x) + x(-7 + x)) = x(1 + -1x) 4x + -1((-7 * 5 + x * 5) + x(-7 + x)) = x(1 + -1x) 4x + -1((-35 + 5x) + x(-7 + x)) = x(1 + -1x) 4x + -1(-35 + 5x + (-7 * x + x * x)) = x(1 + -1x) 4x + -1(-35 + 5x + (-7x + x2)) = x(1 + -1x) Combine like terms: 5x + -7x = -2x 4x + -1(-35 + -2x + x2) = x(1 + -1x) 4x + (-35 * -1 + -2x * -1 + x2 * -1) = x(1 + -1x) 4x + (35 + 2x + -1x2) = x(1 + -1x) Reorder the terms: 35 + 4x + 2x + -1x2 = x(1 + -1x) Combine like terms: 4x + 2x = 6x 35 + 6x + -1x2 = x(1 + -1x) 35 + 6x + -1x2 = (1 * x + -1x * x) 35 + 6x + -1x2 = (1x + -1x2) Add 'x2' to each side of the equation. 35 + 6x + -1x2 + x2 = 1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 35 + 6x + 0 = 1x + -1x2 + x2 35 + 6x = 1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 35 + 6x = 1x + 0 35 + 6x = 1x Solving 35 + 6x = 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 35 + 6x + -1x = 1x + -1x Combine like terms: 6x + -1x = 5x 35 + 5x = 1x + -1x Combine like terms: 1x + -1x = 0 35 + 5x = 0 Add '-35' to each side of the equation. 35 + -35 + 5x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 5x = 0 + -35 5x = 0 + -35 Combine like terms: 0 + -35 = -35 5x = -35 Divide each side by '5'. x = -7 Simplifying x = -7
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