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Simplifying 2a(3a + -4) + -3a(a + -7) = 0 Reorder the terms: 2a(-4 + 3a) + -3a(a + -7) = 0 (-4 * 2a + 3a * 2a) + -3a(a + -7) = 0 (-8a + 6a2) + -3a(a + -7) = 0 Reorder the terms: -8a + 6a2 + -3a(-7 + a) = 0 -8a + 6a2 + (-7 * -3a + a * -3a) = 0 -8a + 6a2 + (21a + -3a2) = 0 Reorder the terms: -8a + 21a + 6a2 + -3a2 = 0 Combine like terms: -8a + 21a = 13a 13a + 6a2 + -3a2 = 0 Combine like terms: 6a2 + -3a2 = 3a2 13a + 3a2 = 0 Solving 13a + 3a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(13 + 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 '(13 + 3a)' equal to zero and attempt to solve: Simplifying 13 + 3a = 0 Solving 13 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3a = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3a = 0 + -13 3a = 0 + -13 Combine like terms: 0 + -13 = -13 3a = -13 Divide each side by '3'. a = -4.333333333 Simplifying a = -4.333333333Solution
a = {0, -4.333333333}
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