(5c-6d)(5c+5d)=

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Solution for (5c-6d)(5c+5d)= equation: 


Simplifying
(5c + -6d)(5c + 5d) = 0

Multiply (5c + -6d) * (5c + 5d)
(5c * (5c + 5d) + -6d * (5c + 5d)) = 0
((5c * 5c + 5d * 5c) + -6d * (5c + 5d)) = 0

Reorder the terms:
((25cd + 25c2) + -6d * (5c + 5d)) = 0
((25cd + 25c2) + -6d * (5c + 5d)) = 0
(25cd + 25c2 + (5c * -6d + 5d * -6d)) = 0
(25cd + 25c2 + (-30cd + -30d2)) = 0

Reorder the terms:
(25cd + -30cd + 25c2 + -30d2) = 0

Combine like terms: 25cd + -30cd = -5cd
(-5cd + 25c2 + -30d2) = 0

Solving
-5cd + 25c2 + -30d2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1cd + 5c2 + -6d2) = 0

Factor a trinomial.
5((5c + -6d)(c + d)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(5c + -6d)' equal to zero and attempt to solve:

Simplifying
5c + -6d = 0

Solving
5c + -6d = 0

Move all terms containing c to the left, all other terms to the right.

Add '6d' to each side of the equation.
5c + -6d + 6d = 0 + 6d

Combine like terms: -6d + 6d = 0
5c + 0 = 0 + 6d
5c = 0 + 6d
Remove the zero:
5c = 6d

Divide each side by '5'.
c = 1.2d

Simplifying
c = 1.2d

Subproblem 2
Set the factor '(c + d)' equal to zero and attempt to solve:

Simplifying
c + d = 0

Solving
c + d = 0

Move all terms containing c to the left, all other terms to the right.

Add '-1d' to each side of the equation.
c + d + -1d = 0 + -1d

Combine like terms: d + -1d = 0
c + 0 = 0 + -1d
c = 0 + -1d
Remove the zero:
c = -1d

Simplifying
c = -1d
Solution
c = {1.2d, -1d}

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