2X^2+33X+45=0

Solution for 2X^2+33X+45=0 equation:

Simplifying
2X2 + 33X + 45 = 0

Reorder the terms:
45 + 33X + 2X2 = 0

Solving
45 + 33X + 2X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(15 + X)(3 + 2X) = 0

Subproblem 1
Set the factor '(15 + X)' equal to zero and attempt to solve:

Simplifying
15 + X = 0

Solving
15 + X = 0

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

Add '-15' to each side of the equation.
15 + -15 + X = 0 + -15

Combine like terms: 15 + -15 = 0
0 + X = 0 + -15
X = 0 + -15

Combine like terms: 0 + -15 = -15
X = -15

Simplifying
X = -15
Subproblem 2
Set the factor '(3 + 2X)' equal to zero and attempt to solve:

Simplifying
3 + 2X = 0

Solving
3 + 2X = 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 + 2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2X = 0 + -3
2X = 0 + -3

Combine like terms: 0 + -3 = -3
2X = -3

Divide each side by '2'.
X = -1.5

Simplifying
X = -1.5
Solution
X = {-15, -1.5}