1+3a=10a^2

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

Simplifying
1 + 3a = 10a2

Solving
1 + 3a = 10a2

Solving for variable 'a'.

Combine like terms: 10a2 + -10a2 = 0
1 + 3a + -10a2 = 0

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

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

Simplifying
1 + -2a = 0

Solving
1 + -2a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2a = 0 + -1

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

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

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

Simplifying
a = 0.5
Subproblem 2
Set the factor '(1 + 5a)' equal to zero and attempt to solve:

Simplifying
1 + 5a = 0

Solving
1 + 5a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5a = 0 + -1

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

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

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

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