(c-80)*(c-80)+(c-40)*(c-40)=c*c

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Solution for (c-80)*(c-80)+(c-40)*(c-40)=c*c equation: 


Simplifying
(c + -80)(c + -80) + (c + -40)(c + -40) = c * c

Reorder the terms:
(-80 + c)(c + -80) + (c + -40)(c + -40) = c * c

Reorder the terms:
(-80 + c)(-80 + c) + (c + -40)(c + -40) = c * c

Multiply (-80 + c) * (-80 + c)
(-80(-80 + c) + c(-80 + c)) + (c + -40)(c + -40) = c * c
((-80 * -80 + c * -80) + c(-80 + c)) + (c + -40)(c + -40) = c * c
((6400 + -80c) + c(-80 + c)) + (c + -40)(c + -40) = c * c
(6400 + -80c + (-80 * c + c * c)) + (c + -40)(c + -40) = c * c
(6400 + -80c + (-80c + c2)) + (c + -40)(c + -40) = c * c

Combine like terms: -80c + -80c = -160c
(6400 + -160c + c2) + (c + -40)(c + -40) = c * c

Reorder the terms:
6400 + -160c + c2 + (-40 + c)(c + -40) = c * c

Reorder the terms:
6400 + -160c + c2 + (-40 + c)(-40 + c) = c * c

Multiply (-40 + c) * (-40 + c)
6400 + -160c + c2 + (-40(-40 + c) + c(-40 + c)) = c * c
6400 + -160c + c2 + ((-40 * -40 + c * -40) + c(-40 + c)) = c * c
6400 + -160c + c2 + ((1600 + -40c) + c(-40 + c)) = c * c
6400 + -160c + c2 + (1600 + -40c + (-40 * c + c * c)) = c * c
6400 + -160c + c2 + (1600 + -40c + (-40c + c2)) = c * c

Combine like terms: -40c + -40c = -80c
6400 + -160c + c2 + (1600 + -80c + c2) = c * c

Reorder the terms:
6400 + 1600 + -160c + -80c + c2 + c2 = c * c

Combine like terms: 6400 + 1600 = 8000
8000 + -160c + -80c + c2 + c2 = c * c

Combine like terms: -160c + -80c = -240c
8000 + -240c + c2 + c2 = c * c

Combine like terms: c2 + c2 = 2c2
8000 + -240c + 2c2 = c * c

Multiply c * c
8000 + -240c + 2c2 = c2

Solving
8000 + -240c + 2c2 = c2

Solving for variable 'c'.

Combine like terms: 2c2 + -1c2 = 1c2
8000 + -240c + 1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
8000 + -240c + 1c2 = 0

Factor a trinomial.
(40 + -1c)(200 + -1c) = 0


Subproblem 1
Set the factor '(40 + -1c)' equal to zero and attempt to solve:

Simplifying
40 + -1c = 0

Solving
40 + -1c = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1c = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1c = 0 + -40
-1c = 0 + -40

Combine like terms: 0 + -40 = -40
-1c = -40

Divide each side by '-1'.
c = 40

Simplifying
c = 40

Subproblem 2
Set the factor '(200 + -1c)' equal to zero and attempt to solve:

Simplifying
200 + -1c = 0

Solving
200 + -1c = 0

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

Add '-200' to each side of the equation.
200 + -200 + -1c = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -1c = 0 + -200
-1c = 0 + -200

Combine like terms: 0 + -200 = -200
-1c = -200

Divide each side by '-1'.
c = 200

Simplifying
c = 200
Solution
c = {40, 200}

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