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Simplifying 6(4x2 + -5x + 2) + 3(-8x2 + 11x + 4) = 0 Reorder the terms: 6(2 + -5x + 4x2) + 3(-8x2 + 11x + 4) = 0 (2 * 6 + -5x * 6 + 4x2 * 6) + 3(-8x2 + 11x + 4) = 0 (12 + -30x + 24x2) + 3(-8x2 + 11x + 4) = 0 Reorder the terms: 12 + -30x + 24x2 + 3(4 + 11x + -8x2) = 0 12 + -30x + 24x2 + (4 * 3 + 11x * 3 + -8x2 * 3) = 0 12 + -30x + 24x2 + (12 + 33x + -24x2) = 0 Reorder the terms: 12 + 12 + -30x + 33x + 24x2 + -24x2 = 0 Combine like terms: 12 + 12 = 24 24 + -30x + 33x + 24x2 + -24x2 = 0 Combine like terms: -30x + 33x = 3x 24 + 3x + 24x2 + -24x2 = 0 Combine like terms: 24x2 + -24x2 = 0 24 + 3x + 0 = 0 24 + 3x = 0 Solving 24 + 3x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + 3x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 3x = 0 + -24 3x = 0 + -24 Combine like terms: 0 + -24 = -24 3x = -24 Divide each side by '3'. x = -8 Simplifying x = -8
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