a^2+3a+15=3-4a

Solution for a^2+3a+15=3-4a equation:

Simplifying
a2 + 3a + 15 = 3 + -4a

Reorder the terms:
15 + 3a + a2 = 3 + -4a

Solving
15 + 3a + a2 = 3 + -4a

Solving for variable 'a'.

Reorder the terms:
15 + -3 + 3a + 4a + a2 = 3 + -4a + -3 + 4a

Combine like terms: 15 + -3 = 12
12 + 3a + 4a + a2 = 3 + -4a + -3 + 4a

Combine like terms: 3a + 4a = 7a
12 + 7a + a2 = 3 + -4a + -3 + 4a

Reorder the terms:
12 + 7a + a2 = 3 + -3 + -4a + 4a

Combine like terms: 3 + -3 = 0
12 + 7a + a2 = 0 + -4a + 4a
12 + 7a + a2 = -4a + 4a

Combine like terms: -4a + 4a = 0
12 + 7a + a2 = 0

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

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

Simplifying
4 + a = 0

Solving
4 + a = 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 + a = 0 + -4

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

Combine like terms: 0 + -4 = -4
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}