3(x-1)-2(x-3)=10

Solution for 3(x-1)-2(x-3)=10 equation:

Simplifying
3(x + -1) + -2(x + -3) = 10

Reorder the terms:
3(-1 + x) + -2(x + -3) = 10
(-1 * 3 + x * 3) + -2(x + -3) = 10
(-3 + 3x) + -2(x + -3) = 10

Reorder the terms:
-3 + 3x + -2(-3 + x) = 10
-3 + 3x + (-3 * -2 + x * -2) = 10
-3 + 3x + (6 + -2x) = 10

Reorder the terms:
-3 + 6 + 3x + -2x = 10

Combine like terms: -3 + 6 = 3
3 + 3x + -2x = 10

Combine like terms: 3x + -2x = 1x
3 + 1x = 10

Solving
3 + 1x = 10

Solving for variable 'x'.

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 = 10 + -3

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

Combine like terms: 10 + -3 = 7
1x = 7

Divide each side by '1'.
x = 7

Simplifying
x = 7