3a^2+a=a^2+10+11

Solution for 3a^2+a=a^2+10+11 equation:

Simplifying
3a2 + a = a2 + 10 + 11

Reorder the terms:
a + 3a2 = a2 + 10 + 11

Reorder the terms:
a + 3a2 = 10 + 11 + a2

Combine like terms: 10 + 11 = 21
a + 3a2 = 21 + a2

Solving
a + 3a2 = 21 + a2

Solving for variable 'a'.

Reorder the terms:
-21 + a + 3a2 + -1a2 = 21 + a2 + -21 + -1a2

Combine like terms: 3a2 + -1a2 = 2a2
-21 + a + 2a2 = 21 + a2 + -21 + -1a2

Reorder the terms:
-21 + a + 2a2 = 21 + -21 + a2 + -1a2

Combine like terms: 21 + -21 = 0
-21 + a + 2a2 = 0 + a2 + -1a2
-21 + a + 2a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-21 + a + 2a2 = 0

Factor a trinomial.
(-7 + -2a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-7 + -2a)' equal to zero and attempt to solve:

Simplifying
-7 + -2a = 0

Solving
-7 + -2a = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2a = 0 + 7
-2a = 0 + 7

Combine like terms: 0 + 7 = 7
-2a = 7

Divide each side by '-2'.
a = -3.5

Simplifying
a = -3.5
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-3.5, 3}