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Simplifying 5(2x + -3) + -6(1 + -5x) + -3x = 15 + -1(8x + 5) + 8(5x + -12) Reorder the terms: 5(-3 + 2x) + -6(1 + -5x) + -3x = 15 + -1(8x + 5) + 8(5x + -12) (-3 * 5 + 2x * 5) + -6(1 + -5x) + -3x = 15 + -1(8x + 5) + 8(5x + -12) (-15 + 10x) + -6(1 + -5x) + -3x = 15 + -1(8x + 5) + 8(5x + -12) -15 + 10x + (1 * -6 + -5x * -6) + -3x = 15 + -1(8x + 5) + 8(5x + -12) -15 + 10x + (-6 + 30x) + -3x = 15 + -1(8x + 5) + 8(5x + -12) Reorder the terms: -15 + -6 + 10x + 30x + -3x = 15 + -1(8x + 5) + 8(5x + -12) Combine like terms: -15 + -6 = -21 -21 + 10x + 30x + -3x = 15 + -1(8x + 5) + 8(5x + -12) Combine like terms: 10x + 30x = 40x -21 + 40x + -3x = 15 + -1(8x + 5) + 8(5x + -12) Combine like terms: 40x + -3x = 37x -21 + 37x = 15 + -1(8x + 5) + 8(5x + -12) Reorder the terms: -21 + 37x = 15 + -1(5 + 8x) + 8(5x + -12) -21 + 37x = 15 + (5 * -1 + 8x * -1) + 8(5x + -12) -21 + 37x = 15 + (-5 + -8x) + 8(5x + -12) Reorder the terms: -21 + 37x = 15 + -5 + -8x + 8(-12 + 5x) -21 + 37x = 15 + -5 + -8x + (-12 * 8 + 5x * 8) -21 + 37x = 15 + -5 + -8x + (-96 + 40x) Reorder the terms: -21 + 37x = 15 + -5 + -96 + -8x + 40x Combine like terms: 15 + -5 = 10 -21 + 37x = 10 + -96 + -8x + 40x Combine like terms: 10 + -96 = -86 -21 + 37x = -86 + -8x + 40x Combine like terms: -8x + 40x = 32x -21 + 37x = -86 + 32x Solving -21 + 37x = -86 + 32x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32x' to each side of the equation. -21 + 37x + -32x = -86 + 32x + -32x Combine like terms: 37x + -32x = 5x -21 + 5x = -86 + 32x + -32x Combine like terms: 32x + -32x = 0 -21 + 5x = -86 + 0 -21 + 5x = -86 Add '21' to each side of the equation. -21 + 21 + 5x = -86 + 21 Combine like terms: -21 + 21 = 0 0 + 5x = -86 + 21 5x = -86 + 21 Combine like terms: -86 + 21 = -65 5x = -65 Divide each side by '5'. x = -13 Simplifying x = -13
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