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Simplifying 2a2 + -4[4b + -2b(b + 3)] = 0 Reorder the terms: 2a2 + -4[4b + -2b(3 + b)] = 0 2a2 + -4[4b + (3 * -2b + b * -2b)] = 0 2a2 + -4[4b + (-6b + -2b2)] = 0 Combine like terms: 4b + -6b = -2b 2a2 + -4[-2b + -2b2] = 0 2a2 + [-2b * -4 + -2b2 * -4] = 0 2a2 + [8b + 8b2] = 0 Solving 2a2 + 8b + 8b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 2a2 + 8b + -8b + 8b2 = 0 + -8b Combine like terms: 8b + -8b = 0 2a2 + 0 + 8b2 = 0 + -8b 2a2 + 8b2 = 0 + -8b Remove the zero: 2a2 + 8b2 = -8b Add '-8b2' to each side of the equation. 2a2 + 8b2 + -8b2 = -8b + -8b2 Combine like terms: 8b2 + -8b2 = 0 2a2 + 0 = -8b + -8b2 2a2 = -8b + -8b2 Divide each side by '2'. a2 = -4b + -4b2 Simplifying a2 = -4b + -4b2 Reorder the terms: a2 + 4b + 4b2 = -4b + 4b + -4b2 + 4b2 Combine like terms: -4b + 4b = 0 a2 + 4b + 4b2 = 0 + -4b2 + 4b2 a2 + 4b + 4b2 = -4b2 + 4b2 Combine like terms: -4b2 + 4b2 = 0 a2 + 4b + 4b2 = 0 Factor a trinomial. (a + 2b)(a + 2b) = 0Subproblem 1
Set the factor '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSubproblem 2
Set the factor '(a + 2b)' equal to zero and attempt to solve: Simplifying a + 2b = 0 Solving a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 a + 0 = 0 + -2b a = 0 + -2b Remove the zero: a = -2b Simplifying a = -2bSolution
a = {-2b, -2b}
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