6y-4(y-3)=3-6(y-9)

Solution for 6y-4(y-3)=3-6(y-9) equation:

Simplifying
6y + -4(y + -3) = 3 + -6(y + -9)

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

Reorder the terms:
12 + 6y + -4y = 3 + -6(y + -9)

Combine like terms: 6y + -4y = 2y
12 + 2y = 3 + -6(y + -9)

Reorder the terms:
12 + 2y = 3 + -6(-9 + y)
12 + 2y = 3 + (-9 * -6 + y * -6)
12 + 2y = 3 + (54 + -6y)

Combine like terms: 3 + 54 = 57
12 + 2y = 57 + -6y

Solving
12 + 2y = 57 + -6y

Solving for variable 'y'.

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

Add '6y' to each side of the equation.
12 + 2y + 6y = 57 + -6y + 6y

Combine like terms: 2y + 6y = 8y
12 + 8y = 57 + -6y + 6y

Combine like terms: -6y + 6y = 0
12 + 8y = 57 + 0
12 + 8y = 57

Add '-12' to each side of the equation.
12 + -12 + 8y = 57 + -12

Combine like terms: 12 + -12 = 0
0 + 8y = 57 + -12
8y = 57 + -12

Combine like terms: 57 + -12 = 45
8y = 45

Divide each side by '8'.
y = 5.625

Simplifying
y = 5.625