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Simplifying (3x + -5)(2x + -7) = 6x2 + 1 Reorder the terms: (-5 + 3x)(2x + -7) = 6x2 + 1 Reorder the terms: (-5 + 3x)(-7 + 2x) = 6x2 + 1 Multiply (-5 + 3x) * (-7 + 2x) (-5(-7 + 2x) + 3x * (-7 + 2x)) = 6x2 + 1 ((-7 * -5 + 2x * -5) + 3x * (-7 + 2x)) = 6x2 + 1 ((35 + -10x) + 3x * (-7 + 2x)) = 6x2 + 1 (35 + -10x + (-7 * 3x + 2x * 3x)) = 6x2 + 1 (35 + -10x + (-21x + 6x2)) = 6x2 + 1 Combine like terms: -10x + -21x = -31x (35 + -31x + 6x2) = 6x2 + 1 Reorder the terms: 35 + -31x + 6x2 = 1 + 6x2 Add '-6x2' to each side of the equation. 35 + -31x + 6x2 + -6x2 = 1 + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 35 + -31x + 0 = 1 + 6x2 + -6x2 35 + -31x = 1 + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 35 + -31x = 1 + 0 35 + -31x = 1 Solving 35 + -31x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -31x = 1 + -35 Combine like terms: 35 + -35 = 0 0 + -31x = 1 + -35 -31x = 1 + -35 Combine like terms: 1 + -35 = -34 -31x = -34 Divide each side by '-31'. x = 1.096774194 Simplifying x = 1.096774194
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