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Simplifying 3a + [-2a(a + b)] = 0 3a + [(a * -2a + b * -2a)] = 0 Reorder the terms: 3a + [(-2ab + -2a2)] = 0 3a + [(-2ab + -2a2)] = 0 3a + [-2ab + -2a2] = 0 Remove brackets around [-2ab + -2a2] 3a + -2ab + -2a2 = 0 Solving 3a + -2ab + -2a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(3 + -2b + -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 '(3 + -2b + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2b + -2a = 0 Reorder the terms: 3 + -2a + -2b = 0 Solving 3 + -2a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -2a + -3 + -2b = 0 + -3 Reorder the terms: 3 + -3 + -2a + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a + -2b = 0 + -3 -2a + -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2a + -2b = -3 Add '2b' to each side of the equation. -2a + -2b + 2b = -3 + 2b Combine like terms: -2b + 2b = 0 -2a + 0 = -3 + 2b -2a = -3 + 2b Divide each side by '-2'. a = 1.5 + -1b Simplifying a = 1.5 + -1bSolution
a = {0, 1.5 + -1b}
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