(5a-3c)(2a-2c)=

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Solution for (5a-3c)(2a-2c)= equation: 


Simplifying
(5a + -3c)(2a + -2c) = 0

Multiply (5a + -3c) * (2a + -2c)
(5a * (2a + -2c) + -3c * (2a + -2c)) = 0
((2a * 5a + -2c * 5a) + -3c * (2a + -2c)) = 0

Reorder the terms:
((-10ac + 10a2) + -3c * (2a + -2c)) = 0
((-10ac + 10a2) + -3c * (2a + -2c)) = 0
(-10ac + 10a2 + (2a * -3c + -2c * -3c)) = 0
(-10ac + 10a2 + (-6ac + 6c2)) = 0

Reorder the terms:
(-10ac + -6ac + 10a2 + 6c2) = 0

Combine like terms: -10ac + -6ac = -16ac
(-16ac + 10a2 + 6c2) = 0

Solving
-16ac + 10a2 + 6c2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8ac + 5a2 + 3c2) = 0

Factor a trinomial.
2((a + -1c)(5a + -3c)) = 0

Ignore the factor 2.

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

Simplifying
a + -1c = 0

Solving
a + -1c = 0

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

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

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

Simplifying
a = c

Subproblem 2
Set the factor '(5a + -3c)' equal to zero and attempt to solve:

Simplifying
5a + -3c = 0

Solving
5a + -3c = 0

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

Add '3c' to each side of the equation.
5a + -3c + 3c = 0 + 3c

Combine like terms: -3c + 3c = 0
5a + 0 = 0 + 3c
5a = 0 + 3c
Remove the zero:
5a = 3c

Divide each side by '5'.
a = 0.6c

Simplifying
a = 0.6c
Solution
a = {c, 0.6c}

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