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Simplifying (2x + 5)(x + 9) = (x + -6)(2x + -3) Reorder the terms: (5 + 2x)(x + 9) = (x + -6)(2x + -3) Reorder the terms: (5 + 2x)(9 + x) = (x + -6)(2x + -3) Multiply (5 + 2x) * (9 + x) (5(9 + x) + 2x * (9 + x)) = (x + -6)(2x + -3) ((9 * 5 + x * 5) + 2x * (9 + x)) = (x + -6)(2x + -3) ((45 + 5x) + 2x * (9 + x)) = (x + -6)(2x + -3) (45 + 5x + (9 * 2x + x * 2x)) = (x + -6)(2x + -3) (45 + 5x + (18x + 2x2)) = (x + -6)(2x + -3) Combine like terms: 5x + 18x = 23x (45 + 23x + 2x2) = (x + -6)(2x + -3) Reorder the terms: 45 + 23x + 2x2 = (-6 + x)(2x + -3) Reorder the terms: 45 + 23x + 2x2 = (-6 + x)(-3 + 2x) Multiply (-6 + x) * (-3 + 2x) 45 + 23x + 2x2 = (-6(-3 + 2x) + x(-3 + 2x)) 45 + 23x + 2x2 = ((-3 * -6 + 2x * -6) + x(-3 + 2x)) 45 + 23x + 2x2 = ((18 + -12x) + x(-3 + 2x)) 45 + 23x + 2x2 = (18 + -12x + (-3 * x + 2x * x)) 45 + 23x + 2x2 = (18 + -12x + (-3x + 2x2)) Combine like terms: -12x + -3x = -15x 45 + 23x + 2x2 = (18 + -15x + 2x2) Add '-2x2' to each side of the equation. 45 + 23x + 2x2 + -2x2 = 18 + -15x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 45 + 23x + 0 = 18 + -15x + 2x2 + -2x2 45 + 23x = 18 + -15x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 45 + 23x = 18 + -15x + 0 45 + 23x = 18 + -15x Solving 45 + 23x = 18 + -15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15x' to each side of the equation. 45 + 23x + 15x = 18 + -15x + 15x Combine like terms: 23x + 15x = 38x 45 + 38x = 18 + -15x + 15x Combine like terms: -15x + 15x = 0 45 + 38x = 18 + 0 45 + 38x = 18 Add '-45' to each side of the equation. 45 + -45 + 38x = 18 + -45 Combine like terms: 45 + -45 = 0 0 + 38x = 18 + -45 38x = 18 + -45 Combine like terms: 18 + -45 = -27 38x = -27 Divide each side by '38'. x = -0.7105263158 Simplifying x = -0.7105263158
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