4a^2+9a=-2

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

Simplifying
4a2 + 9a = -2

Reorder the terms:
9a + 4a2 = -2

Solving
9a + 4a2 = -2

Solving for variable 'a'.

Reorder the terms:
2 + 9a + 4a2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 9a + 4a2 = 0

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

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

Simplifying
1 + 4a = 0

Solving
1 + 4a = 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 + 4a = 0 + -1

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

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

Divide each side by '4'.
a = -0.25

Simplifying
a = -0.25
Solution
a = {-2, -0.25}