5a^2+9a=-4

Solution for 5a^2+9a=-4 equation:

Simplifying
5a2 + 9a = -4

Reorder the terms:
9a + 5a2 = -4

Solving
9a + 5a2 = -4

Solving for variable 'a'.

Reorder the terms:
4 + 9a + 5a2 = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 9a + 5a2 = 0

Factor a trinomial.
(1 + a)(4 + 5a) = 0

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

Simplifying
1 + a = 0

Solving
1 + a = 0

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

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

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

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

Simplifying
a = -1
Subproblem 2
Set the factor '(4 + 5a)' equal to zero and attempt to solve:

Simplifying
4 + 5a = 0

Solving
4 + 5a = 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 + 5a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5a = 0 + -4
5a = 0 + -4

Combine like terms: 0 + -4 = -4
5a = -4

Divide each side by '5'.
a = -0.8

Simplifying
a = -0.8
Solution
a = {-1, -0.8}