-(4c(x-80))=10c(x-10)

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Solution for -(4c(x-80))=10c(x-10) equation: 


Simplifying
-1(4c(x + -80)) = 10c(x + -10)

Reorder the terms:
-1(4c(-80 + x)) = 10c(x + -10)
-1((-80 * 4c + x * 4c)) = 10c(x + -10)
-1((-320c + 4cx)) = 10c(x + -10)
(-320c * -1 + 4cx * -1) = 10c(x + -10)
(320c + -4cx) = 10c(x + -10)

Reorder the terms:
320c + -4cx = 10c(-10 + x)
320c + -4cx = (-10 * 10c + x * 10c)
320c + -4cx = (-100c + 10cx)

Solving
320c + -4cx = -100c + 10cx

Solving for variable 'c'.

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

Add '100c' to each side of the equation.
320c + 100c + -4cx = -100c + 100c + 10cx

Combine like terms: 320c + 100c = 420c
420c + -4cx = -100c + 100c + 10cx

Combine like terms: -100c + 100c = 0
420c + -4cx = 0 + 10cx
420c + -4cx = 10cx

Add '-10cx' to each side of the equation.
420c + -4cx + -10cx = 10cx + -10cx

Combine like terms: -4cx + -10cx = -14cx
420c + -14cx = 10cx + -10cx

Combine like terms: 10cx + -10cx = 0
420c + -14cx = 0

Factor out the Greatest Common Factor (GCF), '14c'.
14c(30 + -1x) = 0

Ignore the factor 14.

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 '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Add 'x' to each side of the equation.
-1x + x = -30 + x

Combine like terms: -1x + x = 0
0 = -30 + x

Simplifying
0 = -30 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
c = {0}

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