a^2=40-3a

Solution for a^2=40-3a equation:

Simplifying
a2 = 40 + -3a

Solving
a2 = 40 + -3a

Solving for variable 'a'.

Reorder the terms:
-40 + 3a + a2 = 40 + -3a + -40 + 3a

Reorder the terms:
-40 + 3a + a2 = 40 + -40 + -3a + 3a

Combine like terms: 40 + -40 = 0
-40 + 3a + a2 = 0 + -3a + 3a
-40 + 3a + a2 = -3a + 3a

Combine like terms: -3a + 3a = 0
-40 + 3a + a2 = 0

Factor a trinomial.
(-8 + -1a)(5 + -1a) = 0

Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve:

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
a = -8

Simplifying
a = -8
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {-8, 5}