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Simplifying (2x + -3)(3x + 1) = (3x + -4)(2x + 2) Reorder the terms: (-3 + 2x)(3x + 1) = (3x + -4)(2x + 2) Reorder the terms: (-3 + 2x)(1 + 3x) = (3x + -4)(2x + 2) Multiply (-3 + 2x) * (1 + 3x) (-3(1 + 3x) + 2x * (1 + 3x)) = (3x + -4)(2x + 2) ((1 * -3 + 3x * -3) + 2x * (1 + 3x)) = (3x + -4)(2x + 2) ((-3 + -9x) + 2x * (1 + 3x)) = (3x + -4)(2x + 2) (-3 + -9x + (1 * 2x + 3x * 2x)) = (3x + -4)(2x + 2) (-3 + -9x + (2x + 6x2)) = (3x + -4)(2x + 2) Combine like terms: -9x + 2x = -7x (-3 + -7x + 6x2) = (3x + -4)(2x + 2) Reorder the terms: -3 + -7x + 6x2 = (-4 + 3x)(2x + 2) Reorder the terms: -3 + -7x + 6x2 = (-4 + 3x)(2 + 2x) Multiply (-4 + 3x) * (2 + 2x) -3 + -7x + 6x2 = (-4(2 + 2x) + 3x * (2 + 2x)) -3 + -7x + 6x2 = ((2 * -4 + 2x * -4) + 3x * (2 + 2x)) -3 + -7x + 6x2 = ((-8 + -8x) + 3x * (2 + 2x)) -3 + -7x + 6x2 = (-8 + -8x + (2 * 3x + 2x * 3x)) -3 + -7x + 6x2 = (-8 + -8x + (6x + 6x2)) Combine like terms: -8x + 6x = -2x -3 + -7x + 6x2 = (-8 + -2x + 6x2) Add '-6x2' to each side of the equation. -3 + -7x + 6x2 + -6x2 = -8 + -2x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -3 + -7x + 0 = -8 + -2x + 6x2 + -6x2 -3 + -7x = -8 + -2x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -3 + -7x = -8 + -2x + 0 -3 + -7x = -8 + -2x Solving -3 + -7x = -8 + -2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2x' to each side of the equation. -3 + -7x + 2x = -8 + -2x + 2x Combine like terms: -7x + 2x = -5x -3 + -5x = -8 + -2x + 2x Combine like terms: -2x + 2x = 0 -3 + -5x = -8 + 0 -3 + -5x = -8 Add '3' to each side of the equation. -3 + 3 + -5x = -8 + 3 Combine like terms: -3 + 3 = 0 0 + -5x = -8 + 3 -5x = -8 + 3 Combine like terms: -8 + 3 = -5 -5x = -5 Divide each side by '-5'. x = 1 Simplifying x = 1
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