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Simplifying 0 = 4a2 + -9ab + -9b2 Reorder the terms: 0 = -9ab + 4a2 + -9b2 Solving 0 = -9ab + 4a2 + -9b2 Solving for variable 'a'. Remove the zero: 9ab + -4a2 + 9b2 = -9ab + 4a2 + -9b2 + 9ab + -4a2 + 9b2 Reorder the terms: 9ab + -4a2 + 9b2 = -9ab + 9ab + 4a2 + -4a2 + -9b2 + 9b2 Combine like terms: -9ab + 9ab = 0 9ab + -4a2 + 9b2 = 0 + 4a2 + -4a2 + -9b2 + 9b2 9ab + -4a2 + 9b2 = 4a2 + -4a2 + -9b2 + 9b2 Combine like terms: 4a2 + -4a2 = 0 9ab + -4a2 + 9b2 = 0 + -9b2 + 9b2 9ab + -4a2 + 9b2 = -9b2 + 9b2 Combine like terms: -9b2 + 9b2 = 0 9ab + -4a2 + 9b2 = 0 Factor a trinomial. (-4a + -3b)(a + -3b) = 0Subproblem 1
Set the factor '(-4a + -3b)' equal to zero and attempt to solve: Simplifying -4a + -3b = 0 Solving -4a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. -4a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 -4a + 0 = 0 + 3b -4a = 0 + 3b Remove the zero: -4a = 3b Divide each side by '-4'. a = -0.75b Simplifying a = -0.75bSubproblem 2
Set the factor '(a + -3b)' equal to zero and attempt to solve: Simplifying a + -3b = 0 Solving a + -3b = 0 Move all terms containing a to the left, all other terms to the right. Add '3b' to each side of the equation. a + -3b + 3b = 0 + 3b Combine like terms: -3b + 3b = 0 a + 0 = 0 + 3b a = 0 + 3b Remove the zero: a = 3b Simplifying a = 3bSolution
a = {-0.75b, 3b}
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