8=c(c-7)

Solution for 8=c(c-7) equation:

Simplifying
8 = c(c + -7)

Reorder the terms:
8 = c(-7 + c)
8 = (-7 * c + c * c)
8 = (-7c + c2)

Solving
8 = -7c + c2

Solving for variable 'c'.

Reorder the terms:
8 + 7c + -1c2 = -7c + 7c + c2 + -1c2

Combine like terms: -7c + 7c = 0
8 + 7c + -1c2 = 0 + c2 + -1c2
8 + 7c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
8 + 7c + -1c2 = 0

Factor a trinomial.
(8 + -1c)(1 + c) = 0

Subproblem 1
Set the factor '(8 + -1c)' equal to zero and attempt to solve:

Simplifying
8 + -1c = 0

Solving
8 + -1c = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1c = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1c = 0 + -8
-1c = 0 + -8

Combine like terms: 0 + -8 = -8
-1c = -8

Divide each side by '-1'.
c = 8

Simplifying
c = 8
Subproblem 2
Set the factor '(1 + c)' equal to zero and attempt to solve:

Simplifying
1 + c = 0

Solving
1 + c = 0

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

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

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

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

Simplifying
c = -1
Solution
c = {8, -1}