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Simplifying 2(3 + -1(3x + 7)(4 + -6c)) = (4c + 5)(9x + -10) + -14c Reorder the terms: 2(3 + -1(7 + 3x)(4 + -6c)) = (4c + 5)(9x + -10) + -14c Multiply (7 + 3x) * (4 + -6c) 2(3 + -1(7(4 + -6c) + 3x * (4 + -6c))) = (4c + 5)(9x + -10) + -14c 2(3 + -1((4 * 7 + -6c * 7) + 3x * (4 + -6c))) = (4c + 5)(9x + -10) + -14c 2(3 + -1((28 + -42c) + 3x * (4 + -6c))) = (4c + 5)(9x + -10) + -14c 2(3 + -1(28 + -42c + (4 * 3x + -6c * 3x))) = (4c + 5)(9x + -10) + -14c Reorder the terms: 2(3 + -1(28 + -42c + (-18cx + 12x))) = (4c + 5)(9x + -10) + -14c 2(3 + -1(28 + -42c + (-18cx + 12x))) = (4c + 5)(9x + -10) + -14c 2(3 + -1(28 + -42c + -18cx + 12x)) = (4c + 5)(9x + -10) + -14c 2(3 + (28 * -1 + -42c * -1 + -18cx * -1 + 12x * -1)) = (4c + 5)(9x + -10) + -14c 2(3 + (-28 + 42c + 18cx + -12x)) = (4c + 5)(9x + -10) + -14c Combine like terms: 3 + -28 = -25 2(-25 + 42c + 18cx + -12x) = (4c + 5)(9x + -10) + -14c (-25 * 2 + 42c * 2 + 18cx * 2 + -12x * 2) = (4c + 5)(9x + -10) + -14c (-50 + 84c + 36cx + -24x) = (4c + 5)(9x + -10) + -14c Reorder the terms: -50 + 84c + 36cx + -24x = (5 + 4c)(9x + -10) + -14c Reorder the terms: -50 + 84c + 36cx + -24x = (5 + 4c)(-10 + 9x) + -14c Multiply (5 + 4c) * (-10 + 9x) -50 + 84c + 36cx + -24x = (5(-10 + 9x) + 4c * (-10 + 9x)) + -14c -50 + 84c + 36cx + -24x = ((-10 * 5 + 9x * 5) + 4c * (-10 + 9x)) + -14c -50 + 84c + 36cx + -24x = ((-50 + 45x) + 4c * (-10 + 9x)) + -14c -50 + 84c + 36cx + -24x = (-50 + 45x + (-10 * 4c + 9x * 4c)) + -14c -50 + 84c + 36cx + -24x = (-50 + 45x + (-40c + 36cx)) + -14c Reorder the terms: -50 + 84c + 36cx + -24x = (-50 + -40c + 36cx + 45x) + -14c -50 + 84c + 36cx + -24x = (-50 + -40c + 36cx + 45x) + -14c Reorder the terms: -50 + 84c + 36cx + -24x = -50 + -40c + -14c + 36cx + 45x Combine like terms: -40c + -14c = -54c -50 + 84c + 36cx + -24x = -50 + -54c + 36cx + 45x Add '50' to each side of the equation. -50 + 84c + 36cx + 50 + -24x = -50 + -54c + 36cx + 50 + 45x Reorder the terms: -50 + 50 + 84c + 36cx + -24x = -50 + -54c + 36cx + 50 + 45x Combine like terms: -50 + 50 = 0 0 + 84c + 36cx + -24x = -50 + -54c + 36cx + 50 + 45x 84c + 36cx + -24x = -50 + -54c + 36cx + 50 + 45x Reorder the terms: 84c + 36cx + -24x = -50 + 50 + -54c + 36cx + 45x Combine like terms: -50 + 50 = 0 84c + 36cx + -24x = 0 + -54c + 36cx + 45x 84c + 36cx + -24x = -54c + 36cx + 45x Add '-36cx' to each side of the equation. 84c + 36cx + -36cx + -24x = -54c + 36cx + -36cx + 45x Combine like terms: 36cx + -36cx = 0 84c + 0 + -24x = -54c + 36cx + -36cx + 45x 84c + -24x = -54c + 36cx + -36cx + 45x Combine like terms: 36cx + -36cx = 0 84c + -24x = -54c + 0 + 45x 84c + -24x = -54c + 45x Solving 84c + -24x = -54c + 45x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '54c' to each side of the equation. 84c + 54c + -24x = -54c + 54c + 45x Combine like terms: 84c + 54c = 138c 138c + -24x = -54c + 54c + 45x Combine like terms: -54c + 54c = 0 138c + -24x = 0 + 45x 138c + -24x = 45x Add '24x' to each side of the equation. 138c + -24x + 24x = 45x + 24x Combine like terms: -24x + 24x = 0 138c + 0 = 45x + 24x 138c = 45x + 24x Combine like terms: 45x + 24x = 69x 138c = 69x Divide each side by '138'. c = 0.5x Simplifying c = 0.5x
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