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Simplifying a(a + 5) = (a + -9)(a + -7) Reorder the terms: a(5 + a) = (a + -9)(a + -7) (5 * a + a * a) = (a + -9)(a + -7) (5a + a2) = (a + -9)(a + -7) Reorder the terms: 5a + a2 = (-9 + a)(a + -7) Reorder the terms: 5a + a2 = (-9 + a)(-7 + a) Multiply (-9 + a) * (-7 + a) 5a + a2 = (-9(-7 + a) + a(-7 + a)) 5a + a2 = ((-7 * -9 + a * -9) + a(-7 + a)) 5a + a2 = ((63 + -9a) + a(-7 + a)) 5a + a2 = (63 + -9a + (-7 * a + a * a)) 5a + a2 = (63 + -9a + (-7a + a2)) Combine like terms: -9a + -7a = -16a 5a + a2 = (63 + -16a + a2) Add '-1a2' to each side of the equation. 5a + a2 + -1a2 = 63 + -16a + a2 + -1a2 Combine like terms: a2 + -1a2 = 0 5a + 0 = 63 + -16a + a2 + -1a2 5a = 63 + -16a + a2 + -1a2 Combine like terms: a2 + -1a2 = 0 5a = 63 + -16a + 0 5a = 63 + -16a Solving 5a = 63 + -16a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '16a' to each side of the equation. 5a + 16a = 63 + -16a + 16a Combine like terms: 5a + 16a = 21a 21a = 63 + -16a + 16a Combine like terms: -16a + 16a = 0 21a = 63 + 0 21a = 63 Divide each side by '21'. a = 3 Simplifying a = 3
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