5(x-1)-2(x+1)=3(x-2)-(x-5)

Solution for 5(x-1)-2(x+1)=3(x-2)-(x-5) equation:

Simplifying
5(x + -1) + -2(x + 1) = 3(x + -2) + -1(x + -5)

Reorder the terms:
5(-1 + x) + -2(x + 1) = 3(x + -2) + -1(x + -5)
(-1 * 5 + x * 5) + -2(x + 1) = 3(x + -2) + -1(x + -5)
(-5 + 5x) + -2(x + 1) = 3(x + -2) + -1(x + -5)

Reorder the terms:
-5 + 5x + -2(1 + x) = 3(x + -2) + -1(x + -5)
-5 + 5x + (1 * -2 + x * -2) = 3(x + -2) + -1(x + -5)
-5 + 5x + (-2 + -2x) = 3(x + -2) + -1(x + -5)

Reorder the terms:
-5 + -2 + 5x + -2x = 3(x + -2) + -1(x + -5)

Combine like terms: -5 + -2 = -7
-7 + 5x + -2x = 3(x + -2) + -1(x + -5)

Combine like terms: 5x + -2x = 3x
-7 + 3x = 3(x + -2) + -1(x + -5)

Reorder the terms:
-7 + 3x = 3(-2 + x) + -1(x + -5)
-7 + 3x = (-2 * 3 + x * 3) + -1(x + -5)
-7 + 3x = (-6 + 3x) + -1(x + -5)

Reorder the terms:
-7 + 3x = -6 + 3x + -1(-5 + x)
-7 + 3x = -6 + 3x + (-5 * -1 + x * -1)
-7 + 3x = -6 + 3x + (5 + -1x)

Reorder the terms:
-7 + 3x = -6 + 5 + 3x + -1x

Combine like terms: -6 + 5 = -1
-7 + 3x = -1 + 3x + -1x

Combine like terms: 3x + -1x = 2x
-7 + 3x = -1 + 2x

Solving
-7 + 3x = -1 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-7 + 3x + -2x = -1 + 2x + -2x

Combine like terms: 3x + -2x = 1x
-7 + 1x = -1 + 2x + -2x

Combine like terms: 2x + -2x = 0
-7 + 1x = -1 + 0
-7 + 1x = -1

Add '7' to each side of the equation.
-7 + 7 + 1x = -1 + 7

Combine like terms: -7 + 7 = 0
0 + 1x = -1 + 7
1x = -1 + 7

Combine like terms: -1 + 7 = 6
1x = 6

Divide each side by '1'.
x = 6

Simplifying
x = 6