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Simplifying 4(3x + 5) + -6(3x + -5) = 12x + 3(2x + -6) Reorder the terms: 4(5 + 3x) + -6(3x + -5) = 12x + 3(2x + -6) (5 * 4 + 3x * 4) + -6(3x + -5) = 12x + 3(2x + -6) (20 + 12x) + -6(3x + -5) = 12x + 3(2x + -6) Reorder the terms: 20 + 12x + -6(-5 + 3x) = 12x + 3(2x + -6) 20 + 12x + (-5 * -6 + 3x * -6) = 12x + 3(2x + -6) 20 + 12x + (30 + -18x) = 12x + 3(2x + -6) Reorder the terms: 20 + 30 + 12x + -18x = 12x + 3(2x + -6) Combine like terms: 20 + 30 = 50 50 + 12x + -18x = 12x + 3(2x + -6) Combine like terms: 12x + -18x = -6x 50 + -6x = 12x + 3(2x + -6) Reorder the terms: 50 + -6x = 12x + 3(-6 + 2x) 50 + -6x = 12x + (-6 * 3 + 2x * 3) 50 + -6x = 12x + (-18 + 6x) Reorder the terms: 50 + -6x = -18 + 12x + 6x Combine like terms: 12x + 6x = 18x 50 + -6x = -18 + 18x Solving 50 + -6x = -18 + 18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18x' to each side of the equation. 50 + -6x + -18x = -18 + 18x + -18x Combine like terms: -6x + -18x = -24x 50 + -24x = -18 + 18x + -18x Combine like terms: 18x + -18x = 0 50 + -24x = -18 + 0 50 + -24x = -18 Add '-50' to each side of the equation. 50 + -50 + -24x = -18 + -50 Combine like terms: 50 + -50 = 0 0 + -24x = -18 + -50 -24x = -18 + -50 Combine like terms: -18 + -50 = -68 -24x = -68 Divide each side by '-24'. x = 2.833333333 Simplifying x = 2.833333333
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