13a^2+3a=10

Solution for 13a^2+3a=10 equation:

Simplifying
13a2 + 3a = 10

Reorder the terms:
3a + 13a2 = 10

Solving
3a + 13a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + 3a + 13a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 3a + 13a2 = 0

Factor a trinomial.
(-1 + -1a)(10 + -13a) = 0

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 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 + -1a = 0 + 1

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

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

Divide each side by '-1'.
a = -1

Simplifying
a = -1
Subproblem 2
Set the factor '(10 + -13a)' equal to zero and attempt to solve:

Simplifying
10 + -13a = 0

Solving
10 + -13a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -13a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -13a = 0 + -10
-13a = 0 + -10

Combine like terms: 0 + -10 = -10
-13a = -10

Divide each side by '-13'.
a = 0.7692307692

Simplifying
a = 0.7692307692
Solution
a = {-1, 0.7692307692}