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Simplifying
(6a + 5b)(6a + -5b) = 0
Multiply (6a + 5b) * (6a + -5b)
(6a * (6a + -5b) + 5b * (6a + -5b)) = 0
((6a * 6a + -5b * 6a) + 5b * (6a + -5b)) = 0
Reorder the terms:
((-30ab + 36a2) + 5b * (6a + -5b)) = 0
((-30ab + 36a2) + 5b * (6a + -5b)) = 0
(-30ab + 36a2 + (6a * 5b + -5b * 5b)) = 0
(-30ab + 36a2 + (30ab + -25b2)) = 0
Reorder the terms:
(-30ab + 30ab + 36a2 + -25b2) = 0
Combine like terms: -30ab + 30ab = 0
(0 + 36a2 + -25b2) = 0
(36a2 + -25b2) = 0
Solving
36a2 + -25b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '25b2' to each side of the equation.
36a2 + -25b2 + 25b2 = 0 + 25b2
Combine like terms: -25b2 + 25b2 = 0
36a2 + 0 = 0 + 25b2
36a2 = 0 + 25b2
Remove the zero:
36a2 = 25b2
Divide each side by '36'.
a2 = 0.6944444444b2
Simplifying
a2 = 0.6944444444b2
Take the square root of each side:
a = {-0.833333333b, 0.833333333b}
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