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

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

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

Reorder the terms:
x + -2(3 + 2x) = 2(x + 1) + -3(3x + -4)
x + (3 * -2 + 2x * -2) = 2(x + 1) + -3(3x + -4)
x + (-6 + -4x) = 2(x + 1) + -3(3x + -4)

Reorder the terms:
-6 + x + -4x = 2(x + 1) + -3(3x + -4)

Combine like terms: x + -4x = -3x
-6 + -3x = 2(x + 1) + -3(3x + -4)

Reorder the terms:
-6 + -3x = 2(1 + x) + -3(3x + -4)
-6 + -3x = (1 * 2 + x * 2) + -3(3x + -4)
-6 + -3x = (2 + 2x) + -3(3x + -4)

Reorder the terms:
-6 + -3x = 2 + 2x + -3(-4 + 3x)
-6 + -3x = 2 + 2x + (-4 * -3 + 3x * -3)
-6 + -3x = 2 + 2x + (12 + -9x)

Reorder the terms:
-6 + -3x = 2 + 12 + 2x + -9x

Combine like terms: 2 + 12 = 14
-6 + -3x = 14 + 2x + -9x

Combine like terms: 2x + -9x = -7x
-6 + -3x = 14 + -7x

Solving
-6 + -3x = 14 + -7x

Solving for variable 'x'.

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

Add '7x' to each side of the equation.
-6 + -3x + 7x = 14 + -7x + 7x

Combine like terms: -3x + 7x = 4x
-6 + 4x = 14 + -7x + 7x

Combine like terms: -7x + 7x = 0
-6 + 4x = 14 + 0
-6 + 4x = 14

Add '6' to each side of the equation.
-6 + 6 + 4x = 14 + 6

Combine like terms: -6 + 6 = 0
0 + 4x = 14 + 6
4x = 14 + 6

Combine like terms: 14 + 6 = 20
4x = 20

Divide each side by '4'.
x = 5

Simplifying
x = 5