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Simplifying 4[5(x + 5) + 7x + 7] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) Reorder the terms: 4[5(5 + x) + 7x + 7] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) 4[(5 * 5 + x * 5) + 7x + 7] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) 4[(25 + 5x) + 7x + 7] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) Reorder the terms: 4[25 + 7 + 5x + 7x] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) Combine like terms: 25 + 7 = 32 4[32 + 5x + 7x] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) Combine like terms: 5x + 7x = 12x 4[32 + 12x] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) [32 * 4 + 12x * 4] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) [128 + 48x] + 6[4(x + -6) + -3(3x + -4)] = 2(5x + 12) Reorder the terms: 128 + 48x + 6[4(-6 + x) + -3(3x + -4)] = 2(5x + 12) 128 + 48x + 6[(-6 * 4 + x * 4) + -3(3x + -4)] = 2(5x + 12) 128 + 48x + 6[(-24 + 4x) + -3(3x + -4)] = 2(5x + 12) Reorder the terms: 128 + 48x + 6[-24 + 4x + -3(-4 + 3x)] = 2(5x + 12) 128 + 48x + 6[-24 + 4x + (-4 * -3 + 3x * -3)] = 2(5x + 12) 128 + 48x + 6[-24 + 4x + (12 + -9x)] = 2(5x + 12) Reorder the terms: 128 + 48x + 6[-24 + 12 + 4x + -9x] = 2(5x + 12) Combine like terms: -24 + 12 = -12 128 + 48x + 6[-12 + 4x + -9x] = 2(5x + 12) Combine like terms: 4x + -9x = -5x 128 + 48x + 6[-12 + -5x] = 2(5x + 12) 128 + 48x + [-12 * 6 + -5x * 6] = 2(5x + 12) 128 + 48x + [-72 + -30x] = 2(5x + 12) Reorder the terms: 128 + -72 + 48x + -30x = 2(5x + 12) Combine like terms: 128 + -72 = 56 56 + 48x + -30x = 2(5x + 12) Combine like terms: 48x + -30x = 18x 56 + 18x = 2(5x + 12) Reorder the terms: 56 + 18x = 2(12 + 5x) 56 + 18x = (12 * 2 + 5x * 2) 56 + 18x = (24 + 10x) Solving 56 + 18x = 24 + 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. 56 + 18x + -10x = 24 + 10x + -10x Combine like terms: 18x + -10x = 8x 56 + 8x = 24 + 10x + -10x Combine like terms: 10x + -10x = 0 56 + 8x = 24 + 0 56 + 8x = 24 Add '-56' to each side of the equation. 56 + -56 + 8x = 24 + -56 Combine like terms: 56 + -56 = 0 0 + 8x = 24 + -56 8x = 24 + -56 Combine like terms: 24 + -56 = -32 8x = -32 Divide each side by '8'. x = -4 Simplifying x = -4
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