4x^2+5x+1=x+4

Solution for 4x^2+5x+1=x+4 equation:

Simplifying
4x2 + 5x + 1 = x + 4

Reorder the terms:
1 + 5x + 4x2 = x + 4

Reorder the terms:
1 + 5x + 4x2 = 4 + x

Solving
1 + 5x + 4x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
1 + -4 + 5x + -1x + 4x2 = 4 + x + -4 + -1x

Combine like terms: 1 + -4 = -3
-3 + 5x + -1x + 4x2 = 4 + x + -4 + -1x

Combine like terms: 5x + -1x = 4x
-3 + 4x + 4x2 = 4 + x + -4 + -1x

Reorder the terms:
-3 + 4x + 4x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-3 + 4x + 4x2 = 0 + x + -1x
-3 + 4x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
-3 + 4x + 4x2 = 0

Factor a trinomial.
(-3 + -2x)(1 + -2x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.5, 0.5}