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Simplifying (4ab + -12a2) = (2b2 + -6ab) Remove parenthesis around (4ab + -12a2) 4ab + -12a2 = (2b2 + -6ab) Reorder the terms: 4ab + -12a2 = (-6ab + 2b2) Remove parenthesis around (-6ab + 2b2) 4ab + -12a2 = -6ab + 2b2 Solving 4ab + -12a2 = -6ab + 2b2 Solving for variable 'a'. Reorder the terms: 4ab + 6ab + -12a2 + -2b2 = -6ab + 2b2 + 6ab + -2b2 Combine like terms: 4ab + 6ab = 10ab 10ab + -12a2 + -2b2 = -6ab + 2b2 + 6ab + -2b2 Reorder the terms: 10ab + -12a2 + -2b2 = -6ab + 6ab + 2b2 + -2b2 Combine like terms: -6ab + 6ab = 0 10ab + -12a2 + -2b2 = 0 + 2b2 + -2b2 10ab + -12a2 + -2b2 = 2b2 + -2b2 Combine like terms: 2b2 + -2b2 = 0 10ab + -12a2 + -2b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5ab + -6a2 + -1b2) = 0 Factor a trinomial. 2((-3a + b)(2a + -1b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3a + b)' equal to zero and attempt to solve: Simplifying -3a + b = 0 Solving -3a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. -3a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 -3a + 0 = 0 + -1b -3a = 0 + -1b Remove the zero: -3a = -1b Divide each side by '-3'. a = 0.3333333333b Simplifying a = 0.3333333333bSubproblem 2
Set the factor '(2a + -1b)' equal to zero and attempt to solve: Simplifying 2a + -1b = 0 Solving 2a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 2a + -1b + b = 0 + b Combine like terms: -1b + b = 0 2a + 0 = 0 + b 2a = 0 + b Remove the zero: 2a = b Divide each side by '2'. a = 0.5b Simplifying a = 0.5bSolution
a = {0.3333333333b, 0.5b}
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