2x^2+53x+180=0

Solution for 2x^2+53x+180=0 equation:

Simplifying
2x2 + 53x + 180 = 0

Reorder the terms:
180 + 53x + 2x2 = 0

Solving
180 + 53x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(45 + 2x)(4 + x) = 0

Subproblem 1
Set the factor '(45 + 2x)' equal to zero and attempt to solve:

Simplifying
45 + 2x = 0

Solving
45 + 2x = 0

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

Add '-45' to each side of the equation.
45 + -45 + 2x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 2x = 0 + -45
2x = 0 + -45

Combine like terms: 0 + -45 = -45
2x = -45

Divide each side by '2'.
x = -22.5

Simplifying
x = -22.5
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-22.5, -4}