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Simplifying (4a + 3b)(4a + 3b) = 0 Multiply (4a + 3b) * (4a + 3b) (4a * (4a + 3b) + 3b * (4a + 3b)) = 0 ((4a * 4a + 3b * 4a) + 3b * (4a + 3b)) = 0 Reorder the terms: ((12ab + 16a2) + 3b * (4a + 3b)) = 0 ((12ab + 16a2) + 3b * (4a + 3b)) = 0 (12ab + 16a2 + (4a * 3b + 3b * 3b)) = 0 (12ab + 16a2 + (12ab + 9b2)) = 0 Reorder the terms: (12ab + 12ab + 16a2 + 9b2) = 0 Combine like terms: 12ab + 12ab = 24ab (24ab + 16a2 + 9b2) = 0 Solving 24ab + 16a2 + 9b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + 3b)(4a + 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 '(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 = -0.75bSolution
a = {-0.75b, -0.75b}
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