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Simplifying 8a(a + -4b) + 5b(a + -4b) = 0 (a * 8a + -4b * 8a) + 5b(a + -4b) = 0 Reorder the terms: (-32ab + 8a2) + 5b(a + -4b) = 0 (-32ab + 8a2) + 5b(a + -4b) = 0 -32ab + 8a2 + (a * 5b + -4b * 5b) = 0 -32ab + 8a2 + (5ab + -20b2) = 0 Reorder the terms: -32ab + 5ab + 8a2 + -20b2 = 0 Combine like terms: -32ab + 5ab = -27ab -27ab + 8a2 + -20b2 = 0 Solving -27ab + 8a2 + -20b2 = 0 Solving for variable 'a'. Factor a trinomial. (a + -4b)(8a + 5b) = 0Subproblem 1
Set the factor '(a + -4b)' equal to zero and attempt to solve: Simplifying a + -4b = 0 Solving a + -4b = 0 Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. a + -4b + 4b = 0 + 4b Combine like terms: -4b + 4b = 0 a + 0 = 0 + 4b a = 0 + 4b Remove the zero: a = 4b Simplifying a = 4bSubproblem 2
Set the factor '(8a + 5b)' equal to zero and attempt to solve: Simplifying 8a + 5b = 0 Solving 8a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 8a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 8a + 0 = 0 + -5b 8a = 0 + -5b Remove the zero: 8a = -5b Divide each side by '8'. a = -0.625b Simplifying a = -0.625bSolution
a = {4b, -0.625b}
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