x+3(x-1)=6-2(2x+3)

Solution for x+3(x-1)=6-2(2x+3) equation:

Simplifying
x + 3(x + -1) = 6 + -2(2x + 3)

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

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

Combine like terms: x + 3x = 4x
-3 + 4x = 6 + -2(2x + 3)

Reorder the terms:
-3 + 4x = 6 + -2(3 + 2x)
-3 + 4x = 6 + (3 * -2 + 2x * -2)
-3 + 4x = 6 + (-6 + -4x)

Combine like terms: 6 + -6 = 0
-3 + 4x = 0 + -4x
-3 + 4x = -4x

Solving
-3 + 4x = -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
-3 + 4x + 4x = -4x + 4x

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

Combine like terms: -4x + 4x = 0
-3 + 8x = 0

Add '3' to each side of the equation.
-3 + 3 + 8x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 8x = 0 + 3
8x = 0 + 3

Combine like terms: 0 + 3 = 3
8x = 3

Divide each side by '8'.
x = 0.375

Simplifying
x = 0.375