18x^2+69x+45=0

Solution for 18x^2+69x+45=0 equation:

Simplifying
18x2 + 69x + 45 = 0

Reorder the terms:
45 + 69x + 18x2 = 0

Solving
45 + 69x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 23x + 6x2) = 0

Factor a trinomial.
3((3 + x)(5 + 6x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {-3, -0.8333333333}