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Simplifying 3a(a + -4) + -2a(5 + a) = 0 Reorder the terms: 3a(-4 + a) + -2a(5 + a) = 0 (-4 * 3a + a * 3a) + -2a(5 + a) = 0 (-12a + 3a2) + -2a(5 + a) = 0 -12a + 3a2 + (5 * -2a + a * -2a) = 0 -12a + 3a2 + (-10a + -2a2) = 0 Reorder the terms: -12a + -10a + 3a2 + -2a2 = 0 Combine like terms: -12a + -10a = -22a -22a + 3a2 + -2a2 = 0 Combine like terms: 3a2 + -2a2 = 1a2 -22a + 1a2 = 0 Solving -22a + 1a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-22 + a) = 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 '(-22 + a)' equal to zero and attempt to solve: Simplifying -22 + a = 0 Solving -22 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + a = 0 + 22 Combine like terms: -22 + 22 = 0 0 + a = 0 + 22 a = 0 + 22 Combine like terms: 0 + 22 = 22 a = 22 Simplifying a = 22Solution
a = {0, 22}
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