a^2+8a+19=3-2a

Solution for a^2+8a+19=3-2a equation:

Simplifying
a2 + 8a + 19 = 3 + -2a

Reorder the terms:
19 + 8a + a2 = 3 + -2a

Solving
19 + 8a + a2 = 3 + -2a

Solving for variable 'a'.

Reorder the terms:
19 + -3 + 8a + 2a + a2 = 3 + -2a + -3 + 2a

Combine like terms: 19 + -3 = 16
16 + 8a + 2a + a2 = 3 + -2a + -3 + 2a

Combine like terms: 8a + 2a = 10a
16 + 10a + a2 = 3 + -2a + -3 + 2a

Reorder the terms:
16 + 10a + a2 = 3 + -3 + -2a + 2a

Combine like terms: 3 + -3 = 0
16 + 10a + a2 = 0 + -2a + 2a
16 + 10a + a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
16 + 10a + a2 = 0

Factor a trinomial.
(8 + a)(2 + a) = 0

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

Simplifying
8 + a = 0

Solving
8 + a = 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 + a = 0 + -8

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

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

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

Simplifying
2 + a = 0

Solving
2 + a = 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 + a = 0 + -2

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

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

Simplifying
a = -2
Solution
a = {-8, -2}