x(5x-4)=1

Solution for x(5x-4)=1 equation:

Simplifying
x(5x + -4) = 1

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

Solving
-4x + 5x2 = 1

Solving for variable 'x'.

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

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

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

Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

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

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

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

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2
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 = {-0.2, 1}