4x^2+61x+222=0

Solution for 4x^2+61x+222=0 equation:

Simplifying
4x2 + 61x + 222 = 0

Reorder the terms:
222 + 61x + 4x2 = 0

Solving
222 + 61x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(37 + 4x)(6 + x) = 0

Subproblem 1
Set the factor '(37 + 4x)' equal to zero and attempt to solve:

Simplifying
37 + 4x = 0

Solving
37 + 4x = 0

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

Add '-37' to each side of the equation.
37 + -37 + 4x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 4x = 0 + -37
4x = 0 + -37

Combine like terms: 0 + -37 = -37
4x = -37

Divide each side by '4'.
x = -9.25

Simplifying
x = -9.25
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

Simplifying
x = -6
Solution
x = {-9.25, -6}