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Simplifying 4a(a + -3) + 5a(2a + 7) = 0 Reorder the terms: 4a(-3 + a) + 5a(2a + 7) = 0 (-3 * 4a + a * 4a) + 5a(2a + 7) = 0 (-12a + 4a2) + 5a(2a + 7) = 0 Reorder the terms: -12a + 4a2 + 5a(7 + 2a) = 0 -12a + 4a2 + (7 * 5a + 2a * 5a) = 0 -12a + 4a2 + (35a + 10a2) = 0 Reorder the terms: -12a + 35a + 4a2 + 10a2 = 0 Combine like terms: -12a + 35a = 23a 23a + 4a2 + 10a2 = 0 Combine like terms: 4a2 + 10a2 = 14a2 23a + 14a2 = 0 Solving 23a + 14a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(23 + 14a) = 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 '(23 + 14a)' equal to zero and attempt to solve: Simplifying 23 + 14a = 0 Solving 23 + 14a = 0 Move all terms containing a to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 14a = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 14a = 0 + -23 14a = 0 + -23 Combine like terms: 0 + -23 = -23 14a = -23 Divide each side by '14'. a = -1.642857143 Simplifying a = -1.642857143Solution
a = {0, -1.642857143}
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