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Simplifying 2a(a + -3) + 5a(2a + 7) = 0 Reorder the terms: 2a(-3 + a) + 5a(2a + 7) = 0 (-3 * 2a + a * 2a) + 5a(2a + 7) = 0 (-6a + 2a2) + 5a(2a + 7) = 0 Reorder the terms: -6a + 2a2 + 5a(7 + 2a) = 0 -6a + 2a2 + (7 * 5a + 2a * 5a) = 0 -6a + 2a2 + (35a + 10a2) = 0 Reorder the terms: -6a + 35a + 2a2 + 10a2 = 0 Combine like terms: -6a + 35a = 29a 29a + 2a2 + 10a2 = 0 Combine like terms: 2a2 + 10a2 = 12a2 29a + 12a2 = 0 Solving 29a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(29 + 12a) = 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 '(29 + 12a)' equal to zero and attempt to solve: Simplifying 29 + 12a = 0 Solving 29 + 12a = 0 Move all terms containing a to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + 12a = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 12a = 0 + -29 12a = 0 + -29 Combine like terms: 0 + -29 = -29 12a = -29 Divide each side by '12'. a = -2.416666667 Simplifying a = -2.416666667Solution
a = {0, -2.416666667}
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