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Simplifying
(4c + 3f)(4c + -3f) = 0
Multiply (4c + 3f) * (4c + -3f)
(4c * (4c + -3f) + 3f * (4c + -3f)) = 0
((4c * 4c + -3f * 4c) + 3f * (4c + -3f)) = 0
Reorder the terms:
((-12cf + 16c2) + 3f * (4c + -3f)) = 0
((-12cf + 16c2) + 3f * (4c + -3f)) = 0
(-12cf + 16c2 + (4c * 3f + -3f * 3f)) = 0
(-12cf + 16c2 + (12cf + -9f2)) = 0
Reorder the terms:
(-12cf + 12cf + 16c2 + -9f2) = 0
Combine like terms: -12cf + 12cf = 0
(0 + 16c2 + -9f2) = 0
(16c2 + -9f2) = 0
Solving
16c2 + -9f2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '9f2' to each side of the equation.
16c2 + -9f2 + 9f2 = 0 + 9f2
Combine like terms: -9f2 + 9f2 = 0
16c2 + 0 = 0 + 9f2
16c2 = 0 + 9f2
Remove the zero:
16c2 = 9f2
Divide each side by '16'.
c2 = 0.5625f2
Simplifying
c2 = 0.5625f2
Take the square root of each side:
c = {-0.75f, 0.75f}
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