1a+3=1a^2-9

Solution for 1a+3=1a^2-9 equation:

Simplifying
1a + 3 = 1a2 + -9

Reorder the terms:
3 + 1a = 1a2 + -9

Reorder the terms:
3 + 1a = -9 + 1a2

Solving
3 + 1a = -9 + 1a2

Solving for variable 'a'.

Reorder the terms:
3 + 9 + 1a + -1a2 = -9 + 1a2 + 9 + -1a2

Combine like terms: 3 + 9 = 12
12 + 1a + -1a2 = -9 + 1a2 + 9 + -1a2

Reorder the terms:
12 + 1a + -1a2 = -9 + 9 + 1a2 + -1a2

Combine like terms: -9 + 9 = 0
12 + 1a + -1a2 = 0 + 1a2 + -1a2
12 + 1a + -1a2 = 1a2 + -1a2

Combine like terms: 1a2 + -1a2 = 0
12 + 1a + -1a2 = 0

Factor a trinomial.
(4 + -1a)(3 + a) = 0

Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {4, -3}