4x^2+x=105

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

Simplifying
4x2 + x = 105

Reorder the terms:
x + 4x2 = 105

Solving
x + 4x2 = 105

Solving for variable 'x'.

Reorder the terms:
-105 + x + 4x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + x + 4x2 = 0

Factor a trinomial.
(-21 + -4x)(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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