3a^2=a+10

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

Simplifying
3a2 = a + 10

Reorder the terms:
3a2 = 10 + a

Solving
3a2 = 10 + a

Solving for variable 'a'.

Reorder the terms:
-10 + -1a + 3a2 = 10 + a + -10 + -1a

Reorder the terms:
-10 + -1a + 3a2 = 10 + -10 + a + -1a

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

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

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

Subproblem 1
Set the factor '(-5 + -3a)' equal to zero and attempt to solve:

Simplifying
-5 + -3a = 0

Solving
-5 + -3a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3a = 0 + 5
-3a = 0 + 5

Combine like terms: 0 + 5 = 5
-3a = 5

Divide each side by '-3'.
a = -1.666666667

Simplifying
a = -1.666666667
Subproblem 2
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-1.666666667, 2}