4c^2=6+10c

Solution for 4c^2=6+10c equation:

Simplifying
4c2 = 6 + 10c

Solving
4c2 = 6 + 10c

Solving for variable 'c'.

Reorder the terms:
-6 + -10c + 4c2 = 6 + 10c + -6 + -10c

Reorder the terms:
-6 + -10c + 4c2 = 6 + -6 + 10c + -10c

Combine like terms: 6 + -6 = 0
-6 + -10c + 4c2 = 0 + 10c + -10c
-6 + -10c + 4c2 = 10c + -10c

Combine like terms: 10c + -10c = 0
-6 + -10c + 4c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5c + 2c2) = 0

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

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

Simplifying
-1 + -2c = 0

Solving
-1 + -2c = 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 + -2c = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2c = 0 + 1
-2c = 0 + 1

Combine like terms: 0 + 1 = 1
-2c = 1

Divide each side by '-2'.
c = -0.5

Simplifying
c = -0.5
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 = {-0.5, 3}