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Simplifying (2a + 5b)(-4a + b) = 0 Multiply (2a + 5b) * (-4a + b) (2a * (-4a + b) + 5b * (-4a + b)) = 0 ((-4a * 2a + b * 2a) + 5b * (-4a + b)) = 0 Reorder the terms: ((2ab + -8a2) + 5b * (-4a + b)) = 0 ((2ab + -8a2) + 5b * (-4a + b)) = 0 (2ab + -8a2 + (-4a * 5b + b * 5b)) = 0 (2ab + -8a2 + (-20ab + 5b2)) = 0 Reorder the terms: (2ab + -20ab + -8a2 + 5b2) = 0 Combine like terms: 2ab + -20ab = -18ab (-18ab + -8a2 + 5b2) = 0 Solving -18ab + -8a2 + 5b2 = 0 Solving for variable 'a'. Factor a trinomial. (-2a + -5b)(4a + -1b) = 0Subproblem 1
Set the factor '(-2a + -5b)' equal to zero and attempt to solve: Simplifying -2a + -5b = 0 Solving -2a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. -2a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 -2a + 0 = 0 + 5b -2a = 0 + 5b Remove the zero: -2a = 5b Divide each side by '-2'. a = -2.5b Simplifying a = -2.5bSubproblem 2
Set the factor '(4a + -1b)' equal to zero and attempt to solve: Simplifying 4a + -1b = 0 Solving 4a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. 4a + -1b + b = 0 + b Combine like terms: -1b + b = 0 4a + 0 = 0 + b 4a = 0 + b Remove the zero: 4a = b Divide each side by '4'. a = 0.25b Simplifying a = 0.25bSolution
a = {-2.5b, 0.25b}
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