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Simplifying 10a3 + -3a2 = 3a3 + -5a2 Reorder the terms: -3a2 + 10a3 = 3a3 + -5a2 Reorder the terms: -3a2 + 10a3 = -5a2 + 3a3 Solving -3a2 + 10a3 = -5a2 + 3a3 Solving for variable 'a'. Reorder the terms: -3a2 + 5a2 + 10a3 + -3a3 = -5a2 + 3a3 + 5a2 + -3a3 Combine like terms: -3a2 + 5a2 = 2a2 2a2 + 10a3 + -3a3 = -5a2 + 3a3 + 5a2 + -3a3 Combine like terms: 10a3 + -3a3 = 7a3 2a2 + 7a3 = -5a2 + 3a3 + 5a2 + -3a3 Reorder the terms: 2a2 + 7a3 = -5a2 + 5a2 + 3a3 + -3a3 Combine like terms: -5a2 + 5a2 = 0 2a2 + 7a3 = 0 + 3a3 + -3a3 2a2 + 7a3 = 3a3 + -3a3 Combine like terms: 3a3 + -3a3 = 0 2a2 + 7a3 = 0 Factor out the Greatest Common Factor (GCF), 'a2'. a2(2 + 7a) = 0Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve: Simplifying a2 = 0 Solving a2 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2 = 0 Take the square root of each side: a = {0}Subproblem 2
Set the factor '(2 + 7a)' equal to zero and attempt to solve: Simplifying 2 + 7a = 0 Solving 2 + 7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 7a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7a = 0 + -2 7a = 0 + -2 Combine like terms: 0 + -2 = -2 7a = -2 Divide each side by '7'. a = -0.2857142857 Simplifying a = -0.2857142857Solution
a = {0, -0.2857142857}
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