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Simplifying (2a + -5)(3a + -2) = (3a + -4)(2a + -3) Reorder the terms: (-5 + 2a)(3a + -2) = (3a + -4)(2a + -3) Reorder the terms: (-5 + 2a)(-2 + 3a) = (3a + -4)(2a + -3) Multiply (-5 + 2a) * (-2 + 3a) (-5(-2 + 3a) + 2a * (-2 + 3a)) = (3a + -4)(2a + -3) ((-2 * -5 + 3a * -5) + 2a * (-2 + 3a)) = (3a + -4)(2a + -3) ((10 + -15a) + 2a * (-2 + 3a)) = (3a + -4)(2a + -3) (10 + -15a + (-2 * 2a + 3a * 2a)) = (3a + -4)(2a + -3) (10 + -15a + (-4a + 6a2)) = (3a + -4)(2a + -3) Combine like terms: -15a + -4a = -19a (10 + -19a + 6a2) = (3a + -4)(2a + -3) Reorder the terms: 10 + -19a + 6a2 = (-4 + 3a)(2a + -3) Reorder the terms: 10 + -19a + 6a2 = (-4 + 3a)(-3 + 2a) Multiply (-4 + 3a) * (-3 + 2a) 10 + -19a + 6a2 = (-4(-3 + 2a) + 3a * (-3 + 2a)) 10 + -19a + 6a2 = ((-3 * -4 + 2a * -4) + 3a * (-3 + 2a)) 10 + -19a + 6a2 = ((12 + -8a) + 3a * (-3 + 2a)) 10 + -19a + 6a2 = (12 + -8a + (-3 * 3a + 2a * 3a)) 10 + -19a + 6a2 = (12 + -8a + (-9a + 6a2)) Combine like terms: -8a + -9a = -17a 10 + -19a + 6a2 = (12 + -17a + 6a2) Add '-6a2' to each side of the equation. 10 + -19a + 6a2 + -6a2 = 12 + -17a + 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 10 + -19a + 0 = 12 + -17a + 6a2 + -6a2 10 + -19a = 12 + -17a + 6a2 + -6a2 Combine like terms: 6a2 + -6a2 = 0 10 + -19a = 12 + -17a + 0 10 + -19a = 12 + -17a Solving 10 + -19a = 12 + -17a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17a' to each side of the equation. 10 + -19a + 17a = 12 + -17a + 17a Combine like terms: -19a + 17a = -2a 10 + -2a = 12 + -17a + 17a Combine like terms: -17a + 17a = 0 10 + -2a = 12 + 0 10 + -2a = 12 Add '-10' to each side of the equation. 10 + -10 + -2a = 12 + -10 Combine like terms: 10 + -10 = 0 0 + -2a = 12 + -10 -2a = 12 + -10 Combine like terms: 12 + -10 = 2 -2a = 2 Divide each side by '-2'. a = -1 Simplifying a = -1
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