6v-54+3(4v-9)=-9(v-3)

Solution for 6v-54+3(4v-9)=-9(v-3) equation:

Simplifying
6v + -54 + 3(4v + -9) = -9(v + -3)

Reorder the terms:
6v + -54 + 3(-9 + 4v) = -9(v + -3)
6v + -54 + (-9 * 3 + 4v * 3) = -9(v + -3)
6v + -54 + (-27 + 12v) = -9(v + -3)

Reorder the terms:
-54 + -27 + 6v + 12v = -9(v + -3)

Combine like terms: -54 + -27 = -81
-81 + 6v + 12v = -9(v + -3)

Combine like terms: 6v + 12v = 18v
-81 + 18v = -9(v + -3)

Reorder the terms:
-81 + 18v = -9(-3 + v)
-81 + 18v = (-3 * -9 + v * -9)
-81 + 18v = (27 + -9v)

Solving
-81 + 18v = 27 + -9v

Solving for variable 'v'.

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

Add '9v' to each side of the equation.
-81 + 18v + 9v = 27 + -9v + 9v

Combine like terms: 18v + 9v = 27v
-81 + 27v = 27 + -9v + 9v

Combine like terms: -9v + 9v = 0
-81 + 27v = 27 + 0
-81 + 27v = 27

Add '81' to each side of the equation.
-81 + 81 + 27v = 27 + 81

Combine like terms: -81 + 81 = 0
0 + 27v = 27 + 81
27v = 27 + 81

Combine like terms: 27 + 81 = 108
27v = 108

Divide each side by '27'.
v = 4

Simplifying
v = 4