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Simplifying 7 + 3x + -1(1 + -1x + x(x + -3)) = x(1 + -1x) Reorder the terms: 7 + 3x + -1(1 + -1x + x(-3 + x)) = x(1 + -1x) 7 + 3x + -1(1 + -1x + (-3 * x + x * x)) = x(1 + -1x) 7 + 3x + -1(1 + -1x + (-3x + x2)) = x(1 + -1x) Combine like terms: -1x + -3x = -4x 7 + 3x + -1(1 + -4x + x2) = x(1 + -1x) 7 + 3x + (1 * -1 + -4x * -1 + x2 * -1) = x(1 + -1x) 7 + 3x + (-1 + 4x + -1x2) = x(1 + -1x) Reorder the terms: 7 + -1 + 3x + 4x + -1x2 = x(1 + -1x) Combine like terms: 7 + -1 = 6 6 + 3x + 4x + -1x2 = x(1 + -1x) Combine like terms: 3x + 4x = 7x 6 + 7x + -1x2 = x(1 + -1x) 6 + 7x + -1x2 = (1 * x + -1x * x) 6 + 7x + -1x2 = (1x + -1x2) Add 'x2' to each side of the equation. 6 + 7x + -1x2 + x2 = 1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 6 + 7x + 0 = 1x + -1x2 + x2 6 + 7x = 1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 6 + 7x = 1x + 0 6 + 7x = 1x Solving 6 + 7x = 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. 6 + 7x + -1x = 1x + -1x Combine like terms: 7x + -1x = 6x 6 + 6x = 1x + -1x Combine like terms: 1x + -1x = 0 6 + 6x = 0 Add '-6' to each side of the equation. 6 + -6 + 6x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6x = 0 + -6 6x = 0 + -6 Combine like terms: 0 + -6 = -6 6x = -6 Divide each side by '6'. x = -1 Simplifying x = -1
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