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Simplifying (2 + -3x)(4x + 3) = (6x + 7)(3 + -2x) Reorder the terms: (2 + -3x)(3 + 4x) = (6x + 7)(3 + -2x) Multiply (2 + -3x) * (3 + 4x) (2(3 + 4x) + -3x * (3 + 4x)) = (6x + 7)(3 + -2x) ((3 * 2 + 4x * 2) + -3x * (3 + 4x)) = (6x + 7)(3 + -2x) ((6 + 8x) + -3x * (3 + 4x)) = (6x + 7)(3 + -2x) (6 + 8x + (3 * -3x + 4x * -3x)) = (6x + 7)(3 + -2x) (6 + 8x + (-9x + -12x2)) = (6x + 7)(3 + -2x) Combine like terms: 8x + -9x = -1x (6 + -1x + -12x2) = (6x + 7)(3 + -2x) Reorder the terms: 6 + -1x + -12x2 = (7 + 6x)(3 + -2x) Multiply (7 + 6x) * (3 + -2x) 6 + -1x + -12x2 = (7(3 + -2x) + 6x * (3 + -2x)) 6 + -1x + -12x2 = ((3 * 7 + -2x * 7) + 6x * (3 + -2x)) 6 + -1x + -12x2 = ((21 + -14x) + 6x * (3 + -2x)) 6 + -1x + -12x2 = (21 + -14x + (3 * 6x + -2x * 6x)) 6 + -1x + -12x2 = (21 + -14x + (18x + -12x2)) Combine like terms: -14x + 18x = 4x 6 + -1x + -12x2 = (21 + 4x + -12x2) Add '12x2' to each side of the equation. 6 + -1x + -12x2 + 12x2 = 21 + 4x + -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 6 + -1x + 0 = 21 + 4x + -12x2 + 12x2 6 + -1x = 21 + 4x + -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 6 + -1x = 21 + 4x + 0 6 + -1x = 21 + 4x Solving 6 + -1x = 21 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 6 + -1x + -4x = 21 + 4x + -4x Combine like terms: -1x + -4x = -5x 6 + -5x = 21 + 4x + -4x Combine like terms: 4x + -4x = 0 6 + -5x = 21 + 0 6 + -5x = 21 Add '-6' to each side of the equation. 6 + -6 + -5x = 21 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 21 + -6 -5x = 21 + -6 Combine like terms: 21 + -6 = 15 -5x = 15 Divide each side by '-5'. x = -3 Simplifying x = -3
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