3(x+5)-6(x-2)=4(x+2)-5(x-4)

Solution for 3(x+5)-6(x-2)=4(x+2)-5(x-4) equation:

Simplifying
3(x + 5) + -6(x + -2) = 4(x + 2) + -5(x + -4)

Reorder the terms:
3(5 + x) + -6(x + -2) = 4(x + 2) + -5(x + -4)
(5 * 3 + x * 3) + -6(x + -2) = 4(x + 2) + -5(x + -4)
(15 + 3x) + -6(x + -2) = 4(x + 2) + -5(x + -4)

Reorder the terms:
15 + 3x + -6(-2 + x) = 4(x + 2) + -5(x + -4)
15 + 3x + (-2 * -6 + x * -6) = 4(x + 2) + -5(x + -4)
15 + 3x + (12 + -6x) = 4(x + 2) + -5(x + -4)

Reorder the terms:
15 + 12 + 3x + -6x = 4(x + 2) + -5(x + -4)

Combine like terms: 15 + 12 = 27
27 + 3x + -6x = 4(x + 2) + -5(x + -4)

Combine like terms: 3x + -6x = -3x
27 + -3x = 4(x + 2) + -5(x + -4)

Reorder the terms:
27 + -3x = 4(2 + x) + -5(x + -4)
27 + -3x = (2 * 4 + x * 4) + -5(x + -4)
27 + -3x = (8 + 4x) + -5(x + -4)

Reorder the terms:
27 + -3x = 8 + 4x + -5(-4 + x)
27 + -3x = 8 + 4x + (-4 * -5 + x * -5)
27 + -3x = 8 + 4x + (20 + -5x)

Reorder the terms:
27 + -3x = 8 + 20 + 4x + -5x

Combine like terms: 8 + 20 = 28
27 + -3x = 28 + 4x + -5x

Combine like terms: 4x + -5x = -1x
27 + -3x = 28 + -1x

Solving
27 + -3x = 28 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
27 + -3x + x = 28 + -1x + x

Combine like terms: -3x + x = -2x
27 + -2x = 28 + -1x + x

Combine like terms: -1x + x = 0
27 + -2x = 28 + 0
27 + -2x = 28

Add '-27' to each side of the equation.
27 + -27 + -2x = 28 + -27

Combine like terms: 27 + -27 = 0
0 + -2x = 28 + -27
-2x = 28 + -27

Combine like terms: 28 + -27 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5