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

Solution for 4(x+2)=2(x-1)+3(x+1) equation:

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

Reorder the terms:
4(2 + x) = 2(x + -1) + 3(x + 1)
(2 * 4 + x * 4) = 2(x + -1) + 3(x + 1)
(8 + 4x) = 2(x + -1) + 3(x + 1)

Reorder the terms:
8 + 4x = 2(-1 + x) + 3(x + 1)
8 + 4x = (-1 * 2 + x * 2) + 3(x + 1)
8 + 4x = (-2 + 2x) + 3(x + 1)

Reorder the terms:
8 + 4x = -2 + 2x + 3(1 + x)
8 + 4x = -2 + 2x + (1 * 3 + x * 3)
8 + 4x = -2 + 2x + (3 + 3x)

Reorder the terms:
8 + 4x = -2 + 3 + 2x + 3x

Combine like terms: -2 + 3 = 1
8 + 4x = 1 + 2x + 3x

Combine like terms: 2x + 3x = 5x
8 + 4x = 1 + 5x

Solving
8 + 4x = 1 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
8 + 4x + -5x = 1 + 5x + -5x

Combine like terms: 4x + -5x = -1x
8 + -1x = 1 + 5x + -5x

Combine like terms: 5x + -5x = 0
8 + -1x = 1 + 0
8 + -1x = 1

Add '-8' to each side of the equation.
8 + -8 + -1x = 1 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 1 + -8
-1x = 1 + -8

Combine like terms: 1 + -8 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7