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Simplifying (9x + -2)(2x + -5) + (3x + 4)(5x + 3) = 3x(11x + -3) Reorder the terms: (-2 + 9x)(2x + -5) + (3x + 4)(5x + 3) = 3x(11x + -3) Reorder the terms: (-2 + 9x)(-5 + 2x) + (3x + 4)(5x + 3) = 3x(11x + -3) Multiply (-2 + 9x) * (-5 + 2x) (-2(-5 + 2x) + 9x * (-5 + 2x)) + (3x + 4)(5x + 3) = 3x(11x + -3) ((-5 * -2 + 2x * -2) + 9x * (-5 + 2x)) + (3x + 4)(5x + 3) = 3x(11x + -3) ((10 + -4x) + 9x * (-5 + 2x)) + (3x + 4)(5x + 3) = 3x(11x + -3) (10 + -4x + (-5 * 9x + 2x * 9x)) + (3x + 4)(5x + 3) = 3x(11x + -3) (10 + -4x + (-45x + 18x2)) + (3x + 4)(5x + 3) = 3x(11x + -3) Combine like terms: -4x + -45x = -49x (10 + -49x + 18x2) + (3x + 4)(5x + 3) = 3x(11x + -3) Reorder the terms: 10 + -49x + 18x2 + (4 + 3x)(5x + 3) = 3x(11x + -3) Reorder the terms: 10 + -49x + 18x2 + (4 + 3x)(3 + 5x) = 3x(11x + -3) Multiply (4 + 3x) * (3 + 5x) 10 + -49x + 18x2 + (4(3 + 5x) + 3x * (3 + 5x)) = 3x(11x + -3) 10 + -49x + 18x2 + ((3 * 4 + 5x * 4) + 3x * (3 + 5x)) = 3x(11x + -3) 10 + -49x + 18x2 + ((12 + 20x) + 3x * (3 + 5x)) = 3x(11x + -3) 10 + -49x + 18x2 + (12 + 20x + (3 * 3x + 5x * 3x)) = 3x(11x + -3) 10 + -49x + 18x2 + (12 + 20x + (9x + 15x2)) = 3x(11x + -3) Combine like terms: 20x + 9x = 29x 10 + -49x + 18x2 + (12 + 29x + 15x2) = 3x(11x + -3) Reorder the terms: 10 + 12 + -49x + 29x + 18x2 + 15x2 = 3x(11x + -3) Combine like terms: 10 + 12 = 22 22 + -49x + 29x + 18x2 + 15x2 = 3x(11x + -3) Combine like terms: -49x + 29x = -20x 22 + -20x + 18x2 + 15x2 = 3x(11x + -3) Combine like terms: 18x2 + 15x2 = 33x2 22 + -20x + 33x2 = 3x(11x + -3) Reorder the terms: 22 + -20x + 33x2 = 3x(-3 + 11x) 22 + -20x + 33x2 = (-3 * 3x + 11x * 3x) 22 + -20x + 33x2 = (-9x + 33x2) Add '-33x2' to each side of the equation. 22 + -20x + 33x2 + -33x2 = -9x + 33x2 + -33x2 Combine like terms: 33x2 + -33x2 = 0 22 + -20x + 0 = -9x + 33x2 + -33x2 22 + -20x = -9x + 33x2 + -33x2 Combine like terms: 33x2 + -33x2 = 0 22 + -20x = -9x + 0 22 + -20x = -9x Solving 22 + -20x = -9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9x' to each side of the equation. 22 + -20x + 9x = -9x + 9x Combine like terms: -20x + 9x = -11x 22 + -11x = -9x + 9x Combine like terms: -9x + 9x = 0 22 + -11x = 0 Add '-22' to each side of the equation. 22 + -22 + -11x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -11x = 0 + -22 -11x = 0 + -22 Combine like terms: 0 + -22 = -22 -11x = -22 Divide each side by '-11'. x = 2 Simplifying x = 2
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