c(x+c)=c(5c+3x)

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Solution for c(x+c)=c(5c+3x) equation: 


Simplifying
c(x + c) = c(5c + 3x)

Reorder the terms:
c(c + x) = c(5c + 3x)
(c * c + x * c) = c(5c + 3x)

Reorder the terms:
(cx + c2) = c(5c + 3x)
(cx + c2) = c(5c + 3x)
cx + c2 = (5c * c + 3x * c)

Reorder the terms:
cx + c2 = (3cx + 5c2)
cx + c2 = (3cx + 5c2)

Solving
cx + c2 = 3cx + 5c2

Solving for variable 'c'.

Reorder the terms:
cx + -3cx + c2 + -5c2 = 3cx + 5c2 + -3cx + -5c2

Combine like terms: cx + -3cx = -2cx
-2cx + c2 + -5c2 = 3cx + 5c2 + -3cx + -5c2

Combine like terms: c2 + -5c2 = -4c2
-2cx + -4c2 = 3cx + 5c2 + -3cx + -5c2

Reorder the terms:
-2cx + -4c2 = 3cx + -3cx + 5c2 + -5c2

Combine like terms: 3cx + -3cx = 0
-2cx + -4c2 = 0 + 5c2 + -5c2
-2cx + -4c2 = 5c2 + -5c2

Combine like terms: 5c2 + -5c2 = 0
-2cx + -4c2 = 0

Factor out the Greatest Common Factor (GCF), '-2c'.
-2c(x + 2c) = 0

Ignore the factor -2.

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

Simplifying
c = 0

Solving
c = 0

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

Simplifying
c = 0

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

Simplifying
x + 2c = 0

Reorder the terms:
2c + x = 0

Solving
2c + x = 0

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

Add '-1x' to each side of the equation.
2c + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
2c + 0 = 0 + -1x
2c = 0 + -1x
Remove the zero:
2c = -1x

Divide each side by '2'.
c = -0.5x

Simplifying
c = -0.5x
Solution
c = {0, -0.5x}

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