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