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Simplifying 3a(4a + -5) + -2a(5a + -4) = 0 Reorder the terms: 3a(-5 + 4a) + -2a(5a + -4) = 0 (-5 * 3a + 4a * 3a) + -2a(5a + -4) = 0 (-15a + 12a2) + -2a(5a + -4) = 0 Reorder the terms: -15a + 12a2 + -2a(-4 + 5a) = 0 -15a + 12a2 + (-4 * -2a + 5a * -2a) = 0 -15a + 12a2 + (8a + -10a2) = 0 Reorder the terms: -15a + 8a + 12a2 + -10a2 = 0 Combine like terms: -15a + 8a = -7a -7a + 12a2 + -10a2 = 0 Combine like terms: 12a2 + -10a2 = 2a2 -7a + 2a2 = 0 Solving -7a + 2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(-7 + 2a) = 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 '(-7 + 2a)' equal to zero and attempt to solve: Simplifying -7 + 2a = 0 Solving -7 + 2a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 2a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2a = 0 + 7 2a = 0 + 7 Combine like terms: 0 + 7 = 7 2a = 7 Divide each side by '2'. a = 3.5 Simplifying a = 3.5Solution
a = {0, 3.5}
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