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Simplifying
(6c + 5f)(6c + -5f) = 0
Multiply (6c + 5f) * (6c + -5f)
(6c * (6c + -5f) + 5f * (6c + -5f)) = 0
((6c * 6c + -5f * 6c) + 5f * (6c + -5f)) = 0
Reorder the terms:
((-30cf + 36c2) + 5f * (6c + -5f)) = 0
((-30cf + 36c2) + 5f * (6c + -5f)) = 0
(-30cf + 36c2 + (6c * 5f + -5f * 5f)) = 0
(-30cf + 36c2 + (30cf + -25f2)) = 0
Reorder the terms:
(-30cf + 30cf + 36c2 + -25f2) = 0
Combine like terms: -30cf + 30cf = 0
(0 + 36c2 + -25f2) = 0
(36c2 + -25f2) = 0
Solving
36c2 + -25f2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '25f2' to each side of the equation.
36c2 + -25f2 + 25f2 = 0 + 25f2
Combine like terms: -25f2 + 25f2 = 0
36c2 + 0 = 0 + 25f2
36c2 = 0 + 25f2
Remove the zero:
36c2 = 25f2
Divide each side by '36'.
c2 = 0.6944444444f2
Simplifying
c2 = 0.6944444444f2
Take the square root of each side:
c = {-0.833333333f, 0.833333333f}
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