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