10(x-3)-x(x-3)=0

Solution for 10(x-3)-x(x-3)=0 equation:

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

Reorder the terms:
10(-3 + x) + -1x(x + -3) = 0
(-3 * 10 + x * 10) + -1x(x + -3) = 0
(-30 + 10x) + -1x(x + -3) = 0

Reorder the terms:
-30 + 10x + -1x(-3 + x) = 0
-30 + 10x + (-3 * -1x + x * -1x) = 0
-30 + 10x + (3x + -1x2) = 0

Combine like terms: 10x + 3x = 13x
-30 + 13x + -1x2 = 0

Solving
-30 + 13x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
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 = {10, 3}