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Simplifying (3x + 1)(2x + -8) + -6x(x + 4) = 0 Reorder the terms: (1 + 3x)(2x + -8) + -6x(x + 4) = 0 Reorder the terms: (1 + 3x)(-8 + 2x) + -6x(x + 4) = 0 Multiply (1 + 3x) * (-8 + 2x) (1(-8 + 2x) + 3x * (-8 + 2x)) + -6x(x + 4) = 0 ((-8 * 1 + 2x * 1) + 3x * (-8 + 2x)) + -6x(x + 4) = 0 ((-8 + 2x) + 3x * (-8 + 2x)) + -6x(x + 4) = 0 (-8 + 2x + (-8 * 3x + 2x * 3x)) + -6x(x + 4) = 0 (-8 + 2x + (-24x + 6x2)) + -6x(x + 4) = 0 Combine like terms: 2x + -24x = -22x (-8 + -22x + 6x2) + -6x(x + 4) = 0 Reorder the terms: -8 + -22x + 6x2 + -6x(4 + x) = 0 -8 + -22x + 6x2 + (4 * -6x + x * -6x) = 0 -8 + -22x + 6x2 + (-24x + -6x2) = 0 Reorder the terms: -8 + -22x + -24x + 6x2 + -6x2 = 0 Combine like terms: -22x + -24x = -46x -8 + -46x + 6x2 + -6x2 = 0 Combine like terms: 6x2 + -6x2 = 0 -8 + -46x + 0 = 0 -8 + -46x = 0 Solving -8 + -46x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -46x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -46x = 0 + 8 -46x = 0 + 8 Combine like terms: 0 + 8 = 8 -46x = 8 Divide each side by '-46'. x = -0.1739130435 Simplifying x = -0.1739130435
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