4x+1=x^2+4

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

Simplifying
4x + 1 = x2 + 4

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

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

Solving
1 + 4x = 4 + x2

Solving for variable 'x'.

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

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

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

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

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

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

Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}