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Simplifying (2x + -3)(6x + 4) = 4x(3x + 5) + 18 Reorder the terms: (-3 + 2x)(6x + 4) = 4x(3x + 5) + 18 Reorder the terms: (-3 + 2x)(4 + 6x) = 4x(3x + 5) + 18 Multiply (-3 + 2x) * (4 + 6x) (-3(4 + 6x) + 2x * (4 + 6x)) = 4x(3x + 5) + 18 ((4 * -3 + 6x * -3) + 2x * (4 + 6x)) = 4x(3x + 5) + 18 ((-12 + -18x) + 2x * (4 + 6x)) = 4x(3x + 5) + 18 (-12 + -18x + (4 * 2x + 6x * 2x)) = 4x(3x + 5) + 18 (-12 + -18x + (8x + 12x2)) = 4x(3x + 5) + 18 Combine like terms: -18x + 8x = -10x (-12 + -10x + 12x2) = 4x(3x + 5) + 18 Reorder the terms: -12 + -10x + 12x2 = 4x(5 + 3x) + 18 -12 + -10x + 12x2 = (5 * 4x + 3x * 4x) + 18 -12 + -10x + 12x2 = (20x + 12x2) + 18 Reorder the terms: -12 + -10x + 12x2 = 18 + 20x + 12x2 Add '-12x2' to each side of the equation. -12 + -10x + 12x2 + -12x2 = 18 + 20x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -10x + 0 = 18 + 20x + 12x2 + -12x2 -12 + -10x = 18 + 20x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -12 + -10x = 18 + 20x + 0 -12 + -10x = 18 + 20x Solving -12 + -10x = 18 + 20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20x' to each side of the equation. -12 + -10x + -20x = 18 + 20x + -20x Combine like terms: -10x + -20x = -30x -12 + -30x = 18 + 20x + -20x Combine like terms: 20x + -20x = 0 -12 + -30x = 18 + 0 -12 + -30x = 18 Add '12' to each side of the equation. -12 + 12 + -30x = 18 + 12 Combine like terms: -12 + 12 = 0 0 + -30x = 18 + 12 -30x = 18 + 12 Combine like terms: 18 + 12 = 30 -30x = 30 Divide each side by '-30'. x = -1 Simplifying x = -1
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