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Simplifying (4 + x)(3 + -1x) = -1x(x + 7) Multiply (4 + x) * (3 + -1x) (4(3 + -1x) + x(3 + -1x)) = -1x(x + 7) ((3 * 4 + -1x * 4) + x(3 + -1x)) = -1x(x + 7) ((12 + -4x) + x(3 + -1x)) = -1x(x + 7) (12 + -4x + (3 * x + -1x * x)) = -1x(x + 7) (12 + -4x + (3x + -1x2)) = -1x(x + 7) Combine like terms: -4x + 3x = -1x (12 + -1x + -1x2) = -1x(x + 7) Reorder the terms: 12 + -1x + -1x2 = -1x(7 + x) 12 + -1x + -1x2 = (7 * -1x + x * -1x) 12 + -1x + -1x2 = (-7x + -1x2) Add 'x2' to each side of the equation. 12 + -1x + -1x2 + x2 = -7x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 12 + -1x + 0 = -7x + -1x2 + x2 12 + -1x = -7x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 12 + -1x = -7x + 0 12 + -1x = -7x Solving 12 + -1x = -7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7x' to each side of the equation. 12 + -1x + 7x = -7x + 7x Combine like terms: -1x + 7x = 6x 12 + 6x = -7x + 7x Combine like terms: -7x + 7x = 0 12 + 6x = 0 Add '-12' to each side of the equation. 12 + -12 + 6x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6x = 0 + -12 6x = 0 + -12 Combine like terms: 0 + -12 = -12 6x = -12 Divide each side by '6'. x = -2 Simplifying x = -2
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