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Simplifying (4x + 3)(6x + -5) = (2x + 3)(12x + -13) Reorder the terms: (3 + 4x)(6x + -5) = (2x + 3)(12x + -13) Reorder the terms: (3 + 4x)(-5 + 6x) = (2x + 3)(12x + -13) Multiply (3 + 4x) * (-5 + 6x) (3(-5 + 6x) + 4x * (-5 + 6x)) = (2x + 3)(12x + -13) ((-5 * 3 + 6x * 3) + 4x * (-5 + 6x)) = (2x + 3)(12x + -13) ((-15 + 18x) + 4x * (-5 + 6x)) = (2x + 3)(12x + -13) (-15 + 18x + (-5 * 4x + 6x * 4x)) = (2x + 3)(12x + -13) (-15 + 18x + (-20x + 24x2)) = (2x + 3)(12x + -13) Combine like terms: 18x + -20x = -2x (-15 + -2x + 24x2) = (2x + 3)(12x + -13) Reorder the terms: -15 + -2x + 24x2 = (3 + 2x)(12x + -13) Reorder the terms: -15 + -2x + 24x2 = (3 + 2x)(-13 + 12x) Multiply (3 + 2x) * (-13 + 12x) -15 + -2x + 24x2 = (3(-13 + 12x) + 2x * (-13 + 12x)) -15 + -2x + 24x2 = ((-13 * 3 + 12x * 3) + 2x * (-13 + 12x)) -15 + -2x + 24x2 = ((-39 + 36x) + 2x * (-13 + 12x)) -15 + -2x + 24x2 = (-39 + 36x + (-13 * 2x + 12x * 2x)) -15 + -2x + 24x2 = (-39 + 36x + (-26x + 24x2)) Combine like terms: 36x + -26x = 10x -15 + -2x + 24x2 = (-39 + 10x + 24x2) Add '-24x2' to each side of the equation. -15 + -2x + 24x2 + -24x2 = -39 + 10x + 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -15 + -2x + 0 = -39 + 10x + 24x2 + -24x2 -15 + -2x = -39 + 10x + 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -15 + -2x = -39 + 10x + 0 -15 + -2x = -39 + 10x Solving -15 + -2x = -39 + 10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. -15 + -2x + -10x = -39 + 10x + -10x Combine like terms: -2x + -10x = -12x -15 + -12x = -39 + 10x + -10x Combine like terms: 10x + -10x = 0 -15 + -12x = -39 + 0 -15 + -12x = -39 Add '15' to each side of the equation. -15 + 15 + -12x = -39 + 15 Combine like terms: -15 + 15 = 0 0 + -12x = -39 + 15 -12x = -39 + 15 Combine like terms: -39 + 15 = -24 -12x = -24 Divide each side by '-12'. x = 2 Simplifying x = 2
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