(2x-5)x-2=1

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

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

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

Reorder the terms for easier multiplication:
x(-5 + 2x) + -2 = 1
(-5 * x + 2x * x) + -2 = 1
(-5x + 2x2) + -2 = 1

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

Solving
-2 + -5x + 2x2 = 1

Solving for variable 'x'.

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

Combine like terms: -2 + -1 = -3
-3 + -5x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-3 + -5x + 2x2 = 0

Factor a trinomial.
(-1 + -2x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}