x(2x-5)=6-x

Solution for x(2x-5)=6-x equation:

Simplifying
x(2x + -5) = 6 + -1x

Reorder the terms:
x(-5 + 2x) = 6 + -1x
(-5 * x + 2x * x) = 6 + -1x
(-5x + 2x2) = 6 + -1x

Solving
-5x + 2x2 = 6 + -1x

Solving for variable 'x'.

Reorder the terms:
-6 + -5x + x + 2x2 = 6 + -1x + -6 + x

Combine like terms: -5x + x = -4x
-6 + -4x + 2x2 = 6 + -1x + -6 + x

Reorder the terms:
-6 + -4x + 2x2 = 6 + -6 + -1x + x

Combine like terms: 6 + -6 = 0
-6 + -4x + 2x2 = 0 + -1x + x
-6 + -4x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-6 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -2x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(3 + -1x)) = 0

Ignore the factor 2.
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 '(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 = {-1, 3}