5x^2-x^2-5x+1=0

Solution for 5x^2-x^2-5x+1=0 equation:

Simplifying
5x2 + -1x2 + -5x + 1 = 0

Reorder the terms:
1 + -5x + 5x2 + -1x2 = 0

Combine like terms: 5x2 + -1x2 = 4x2
1 + -5x + 4x2 = 0

Solving
1 + -5x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -4x)(1 + -1x) = 0

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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
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 = {0.25, 1}