x^2+4=6x-1

Solution for x^2+4=6x-1 equation:

Simplifying
x2 + 4 = 6x + -1

Reorder the terms:
4 + x2 = 6x + -1

Reorder the terms:
4 + x2 = -1 + 6x

Solving
4 + x2 = -1 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + 1 + -6x + x2 = -1 + 6x + 1 + -6x

Combine like terms: 4 + 1 = 5
5 + -6x + x2 = -1 + 6x + 1 + -6x

Reorder the terms:
5 + -6x + x2 = -1 + 1 + 6x + -6x

Combine like terms: -1 + 1 = 0
5 + -6x + x2 = 0 + 6x + -6x
5 + -6x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
5 + -6x + x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 0

Subproblem 1
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
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 = {1, 5}