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Simplifying (4a + -1b)(5a + 2b) = 0 Multiply (4a + -1b) * (5a + 2b) (4a * (5a + 2b) + -1b * (5a + 2b)) = 0 ((5a * 4a + 2b * 4a) + -1b * (5a + 2b)) = 0 Reorder the terms: ((8ab + 20a2) + -1b * (5a + 2b)) = 0 ((8ab + 20a2) + -1b * (5a + 2b)) = 0 (8ab + 20a2 + (5a * -1b + 2b * -1b)) = 0 (8ab + 20a2 + (-5ab + -2b2)) = 0 Reorder the terms: (8ab + -5ab + 20a2 + -2b2) = 0 Combine like terms: 8ab + -5ab = 3ab (3ab + 20a2 + -2b2) = 0 Solving 3ab + 20a2 + -2b2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -1b)(5a + 2b) = 0Subproblem 1
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 = 0.25bSubproblem 2
Set the factor '(5a + 2b)' equal to zero and attempt to solve: Simplifying 5a + 2b = 0 Solving 5a + 2b = 0 Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. 5a + 2b + -2b = 0 + -2b Combine like terms: 2b + -2b = 0 5a + 0 = 0 + -2b 5a = 0 + -2b Remove the zero: 5a = -2b Divide each side by '5'. a = -0.4b Simplifying a = -0.4bSolution
a = {0.25b, -0.4b}
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