(2x-1)(x-5)+1=2x

Solution for (2x-1)(x-5)+1=2x equation:

Simplifying
(2x + -1)(x + -5) + 1 = 2x

Reorder the terms:
(-1 + 2x)(x + -5) + 1 = 2x

Reorder the terms:
(-1 + 2x)(-5 + x) + 1 = 2x

Multiply (-1 + 2x) * (-5 + x)
(-1(-5 + x) + 2x * (-5 + x)) + 1 = 2x
((-5 * -1 + x * -1) + 2x * (-5 + x)) + 1 = 2x
((5 + -1x) + 2x * (-5 + x)) + 1 = 2x
(5 + -1x + (-5 * 2x + x * 2x)) + 1 = 2x
(5 + -1x + (-10x + 2x2)) + 1 = 2x

Combine like terms: -1x + -10x = -11x
(5 + -11x + 2x2) + 1 = 2x

Reorder the terms:
5 + 1 + -11x + 2x2 = 2x

Combine like terms: 5 + 1 = 6
6 + -11x + 2x2 = 2x

Solving
6 + -11x + 2x2 = 2x

Solving for variable 'x'.

Reorder the terms:
6 + -11x + -2x + 2x2 = 2x + -2x

Combine like terms: -11x + -2x = -13x
6 + -13x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -13x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0.5, 6}