4(x-1)+3(y+2)=5(x-4)

Solution for 4(x-1)+3(y+2)=5(x-4) equation:

Simplifying
4(x + -1) + 3(y + 2) = 5(x + -4)

Reorder the terms:
4(-1 + x) + 3(y + 2) = 5(x + -4)
(-1 * 4 + x * 4) + 3(y + 2) = 5(x + -4)
(-4 + 4x) + 3(y + 2) = 5(x + -4)

Reorder the terms:
-4 + 4x + 3(2 + y) = 5(x + -4)
-4 + 4x + (2 * 3 + y * 3) = 5(x + -4)
-4 + 4x + (6 + 3y) = 5(x + -4)

Reorder the terms:
-4 + 6 + 4x + 3y = 5(x + -4)

Combine like terms: -4 + 6 = 2
2 + 4x + 3y = 5(x + -4)

Reorder the terms:
2 + 4x + 3y = 5(-4 + x)
2 + 4x + 3y = (-4 * 5 + x * 5)
2 + 4x + 3y = (-20 + 5x)

Solving
2 + 4x + 3y = -20 + 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.
2 + 4x + -5x + 3y = -20 + 5x + -5x

Combine like terms: 4x + -5x = -1x
2 + -1x + 3y = -20 + 5x + -5x

Combine like terms: 5x + -5x = 0
2 + -1x + 3y = -20 + 0
2 + -1x + 3y = -20

Add '-2' to each side of the equation.
2 + -1x + -2 + 3y = -20 + -2

Reorder the terms:
2 + -2 + -1x + 3y = -20 + -2

Combine like terms: 2 + -2 = 0
0 + -1x + 3y = -20 + -2
-1x + 3y = -20 + -2

Combine like terms: -20 + -2 = -22
-1x + 3y = -22

Add '-3y' to each side of the equation.
-1x + 3y + -3y = -22 + -3y

Combine like terms: 3y + -3y = 0
-1x + 0 = -22 + -3y
-1x = -22 + -3y

Divide each side by '-1'.
x = 22 + 3y

Simplifying
x = 22 + 3y