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