1+3c=10c^2

Solution for 1+3c=10c^2 equation:

Simplifying
1 + 3c = 10c2

Solving
1 + 3c = 10c2

Solving for variable 'c'.

Combine like terms: 10c2 + -10c2 = 0
1 + 3c + -10c2 = 0

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

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 '(1 + 5c)' equal to zero and attempt to solve:

Simplifying
1 + 5c = 0

Solving
1 + 5c = 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 + 5c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5c = 0 + -1
5c = 0 + -1

Combine like terms: 0 + -1 = -1
5c = -1

Divide each side by '5'.
c = -0.2

Simplifying
c = -0.2
Solution
c = {0.5, -0.2}