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Simplifying
(2a + -1b)(2a + b) = 0
Multiply (2a + -1b) * (2a + b)
(2a * (2a + b) + -1b * (2a + b)) = 0
((2a * 2a + b * 2a) + -1b * (2a + b)) = 0
Reorder the terms:
((2ab + 4a2) + -1b * (2a + b)) = 0
((2ab + 4a2) + -1b * (2a + b)) = 0
(2ab + 4a2 + (2a * -1b + b * -1b)) = 0
(2ab + 4a2 + (-2ab + -1b2)) = 0
Reorder the terms:
(2ab + -2ab + 4a2 + -1b2) = 0
Combine like terms: 2ab + -2ab = 0
(0 + 4a2 + -1b2) = 0
(4a2 + -1b2) = 0
Solving
4a2 + -1b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add 'b2' to each side of the equation.
4a2 + -1b2 + b2 = 0 + b2
Combine like terms: -1b2 + b2 = 0
4a2 + 0 = 0 + b2
4a2 = 0 + b2
Remove the zero:
4a2 = b2
Divide each side by '4'.
a2 = 0.25b2
Simplifying
a2 = 0.25b2
Take the square root of each side:
a = {-0.5b, 0.5b}
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