(a-c)(a+c)-c(3a-c)=

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Solution for (a-c)(a+c)-c(3a-c)= equation: 


Simplifying
(a + -1c)(a + c) + -1c(3a + -1c) = 0

Multiply (a + -1c) * (a + c)
(a(a + c) + -1c * (a + c)) + -1c(3a + -1c) = 0
((a * a + c * a) + -1c * (a + c)) + -1c(3a + -1c) = 0

Reorder the terms:
((ac + a2) + -1c * (a + c)) + -1c(3a + -1c) = 0
((ac + a2) + -1c * (a + c)) + -1c(3a + -1c) = 0
(ac + a2 + (a * -1c + c * -1c)) + -1c(3a + -1c) = 0
(ac + a2 + (-1ac + -1c2)) + -1c(3a + -1c) = 0

Reorder the terms:
(ac + -1ac + a2 + -1c2) + -1c(3a + -1c) = 0

Combine like terms: ac + -1ac = 0
(0 + a2 + -1c2) + -1c(3a + -1c) = 0
(a2 + -1c2) + -1c(3a + -1c) = 0
a2 + -1c2 + (3a * -1c + -1c * -1c) = 0
a2 + -1c2 + (-3ac + 1c2) = 0

Reorder the terms:
-3ac + a2 + -1c2 + 1c2 = 0

Combine like terms: -1c2 + 1c2 = 0
-3ac + a2 + 0 = 0
-3ac + a2 = 0

Solving
-3ac + a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-3c + a) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

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

Simplifying
-3c + a = 0

Reorder the terms:
a + -3c = 0

Solving
a + -3c = 0

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

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

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

Simplifying
a = 3c
Solution
a = {0, 3c}

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