4a^2+17a+18=0

Solution for 4a^2+17a+18=0 equation:

Simplifying
4a2 + 17a + 18 = 0

Reorder the terms:
18 + 17a + 4a2 = 0

Solving
18 + 17a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9 + 4a)(2 + a) = 0

Subproblem 1
Set the factor '(9 + 4a)' equal to zero and attempt to solve:

Simplifying
9 + 4a = 0

Solving
9 + 4a = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4a = 0 + -9

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

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

Divide each side by '4'.
a = -2.25

Simplifying
a = -2.25
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 = {-2.25, -2}