10c^2=24+22c

Solution for 10c^2=24+22c equation:

Simplifying
10c2 = 24 + 22c

Solving
10c2 = 24 + 22c

Solving for variable 'c'.

Reorder the terms:
-24 + -22c + 10c2 = 24 + 22c + -24 + -22c

Reorder the terms:
-24 + -22c + 10c2 = 24 + -24 + 22c + -22c

Combine like terms: 24 + -24 = 0
-24 + -22c + 10c2 = 0 + 22c + -22c
-24 + -22c + 10c2 = 22c + -22c

Combine like terms: 22c + -22c = 0
-24 + -22c + 10c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + -11c + 5c2) = 0

Factor a trinomial.
2((-4 + -5c)(3 + -1c)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -5c)' equal to zero and attempt to solve:

Simplifying
-4 + -5c = 0

Solving
-4 + -5c = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5c = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5c = 0 + 4
-5c = 0 + 4

Combine like terms: 0 + 4 = 4
-5c = 4

Divide each side by '-5'.
c = -0.8

Simplifying
c = -0.8
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 = {-0.8, 3}