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Simplifying
(3c + 5t)(3c + -5t) = 0
Multiply (3c + 5t) * (3c + -5t)
(3c * (3c + -5t) + 5t * (3c + -5t)) = 0
((3c * 3c + -5t * 3c) + 5t * (3c + -5t)) = 0
Reorder the terms:
((-15ct + 9c2) + 5t * (3c + -5t)) = 0
((-15ct + 9c2) + 5t * (3c + -5t)) = 0
(-15ct + 9c2 + (3c * 5t + -5t * 5t)) = 0
(-15ct + 9c2 + (15ct + -25t2)) = 0
Reorder the terms:
(-15ct + 15ct + 9c2 + -25t2) = 0
Combine like terms: -15ct + 15ct = 0
(0 + 9c2 + -25t2) = 0
(9c2 + -25t2) = 0
Solving
9c2 + -25t2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '25t2' to each side of the equation.
9c2 + -25t2 + 25t2 = 0 + 25t2
Combine like terms: -25t2 + 25t2 = 0
9c2 + 0 = 0 + 25t2
9c2 = 0 + 25t2
Remove the zero:
9c2 = 25t2
Divide each side by '9'.
c2 = 2.777777778t2
Simplifying
c2 = 2.777777778t2
Take the square root of each side:
c = {-1.666666667t, 1.666666667t}
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