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Simplifying a(6a + 1) = 2a(2 + -2.5a) Reorder the terms: a(1 + 6a) = 2a(2 + -2.5a) (1 * a + 6a * a) = 2a(2 + -2.5a) (1a + 6a2) = 2a(2 + -2.5a) 1a + 6a2 = (2 * 2a + -2.5a * 2a) 1a + 6a2 = (4a + -5a2) Solving 1a + 6a2 = 4a + -5a2 Solving for variable 'a'. Reorder the terms: 1a + -4a + 6a2 + 5a2 = 4a + -5a2 + -4a + 5a2 Combine like terms: 1a + -4a = -3a -3a + 6a2 + 5a2 = 4a + -5a2 + -4a + 5a2 Combine like terms: 6a2 + 5a2 = 11a2 -3a + 11a2 = 4a + -5a2 + -4a + 5a2 Reorder the terms: -3a + 11a2 = 4a + -4a + -5a2 + 5a2 Combine like terms: 4a + -4a = 0 -3a + 11a2 = 0 + -5a2 + 5a2 -3a + 11a2 = -5a2 + 5a2 Combine like terms: -5a2 + 5a2 = 0 -3a + 11a2 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-3 + 11a) = 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 '(-3 + 11a)' equal to zero and attempt to solve: Simplifying -3 + 11a = 0 Solving -3 + 11a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 11a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 11a = 0 + 3 11a = 0 + 3 Combine like terms: 0 + 3 = 3 11a = 3 Divide each side by '11'. a = 0.2727272727 Simplifying a = 0.2727272727Solution
a = {0, 0.2727272727}
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