4x^2+41x+105=0

Solution for 4x^2+41x+105=0 equation:

Simplifying
4x2 + 41x + 105 = 0

Reorder the terms:
105 + 41x + 4x2 = 0

Solving
105 + 41x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(21 + 4x)(5 + x) = 0

Subproblem 1
Set the factor '(21 + 4x)' equal to zero and attempt to solve:

Simplifying
21 + 4x = 0

Solving
21 + 4x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 4x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4x = 0 + -21
4x = 0 + -21

Combine like terms: 0 + -21 = -21
4x = -21

Divide each side by '4'.
x = -5.25

Simplifying
x = -5.25
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-5.25, -5}