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Simplifying 5a(a + 2) = a(2a + 5) Reorder the terms: 5a(2 + a) = a(2a + 5) (2 * 5a + a * 5a) = a(2a + 5) (10a + 5a2) = a(2a + 5) Reorder the terms: 10a + 5a2 = a(5 + 2a) 10a + 5a2 = (5 * a + 2a * a) 10a + 5a2 = (5a + 2a2) Solving 10a + 5a2 = 5a + 2a2 Solving for variable 'a'. Reorder the terms: 10a + -5a + 5a2 + -2a2 = 5a + 2a2 + -5a + -2a2 Combine like terms: 10a + -5a = 5a 5a + 5a2 + -2a2 = 5a + 2a2 + -5a + -2a2 Combine like terms: 5a2 + -2a2 = 3a2 5a + 3a2 = 5a + 2a2 + -5a + -2a2 Reorder the terms: 5a + 3a2 = 5a + -5a + 2a2 + -2a2 Combine like terms: 5a + -5a = 0 5a + 3a2 = 0 + 2a2 + -2a2 5a + 3a2 = 2a2 + -2a2 Combine like terms: 2a2 + -2a2 = 0 5a + 3a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(5 + 3a) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(5 + 3a)' equal to zero and attempt to solve: Simplifying 5 + 3a = 0 Solving 5 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3a = 0 + -5 3a = 0 + -5 Combine like terms: 0 + -5 = -5 3a = -5 Divide each side by '3'. a = -1.666666667 Simplifying a = -1.666666667Solution
a = {0, -1.666666667}
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