=5c^2-50c+105

Solution for =5c^2-50c+105 equation:

Simplifying
0 = 5c2 + -50c + 105

Reorder the terms:
0 = 105 + -50c + 5c2

Solving
0 = 105 + -50c + 5c2

Solving for variable 'c'.

Combine like terms: 0 + -105 = -105
-105 + 50c + -5c2 = 105 + -50c + 5c2 + -105 + 50c + -5c2

Reorder the terms:
-105 + 50c + -5c2 = 105 + -105 + -50c + 50c + 5c2 + -5c2

Combine like terms: 105 + -105 = 0
-105 + 50c + -5c2 = 0 + -50c + 50c + 5c2 + -5c2
-105 + 50c + -5c2 = -50c + 50c + 5c2 + -5c2

Combine like terms: -50c + 50c = 0
-105 + 50c + -5c2 = 0 + 5c2 + -5c2
-105 + 50c + -5c2 = 5c2 + -5c2

Combine like terms: 5c2 + -5c2 = 0
-105 + 50c + -5c2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + 10c + -1c2) = 0

Factor a trinomial.
5((-7 + c)(3 + -1c)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + c)' equal to zero and attempt to solve:

Simplifying
-7 + c = 0

Solving
-7 + c = 0

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

Add '7' to each side of the equation.
-7 + 7 + c = 0 + 7

Combine like terms: -7 + 7 = 0
0 + c = 0 + 7
c = 0 + 7

Combine like terms: 0 + 7 = 7
c = 7

Simplifying
c = 7
Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1c = 0 + -3
-1c = 0 + -3

Combine like terms: 0 + -3 = -3
-1c = -3

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {7, 3}