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