x(x-1)-3(x^2-x)=

Solution for x(x-1)-3(x^2-x)= equation:

Simplifying
x(x + -1) + -3(x2 + -1x) = 0

Reorder the terms:
x(-1 + x) + -3(x2 + -1x) = 0
(-1 * x + x * x) + -3(x2 + -1x) = 0
(-1x + x2) + -3(x2 + -1x) = 0

Reorder the terms:
-1x + x2 + -3(-1x + x2) = 0
-1x + x2 + (-1x * -3 + x2 * -3) = 0
-1x + x2 + (3x + -3x2) = 0

Reorder the terms:
-1x + 3x + x2 + -3x2 = 0

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

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

Solving
2x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + -1x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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, 1}