3[z-(3z+8)+6]=3(z-7)

Solution for 3[z-(3z+8)+6]=3(z-7) equation:

Simplifying
3[z + -1(3z + 8) + 6] = 3(z + -7)

Reorder the terms:
3[z + -1(8 + 3z) + 6] = 3(z + -7)
3[z + (8 * -1 + 3z * -1) + 6] = 3(z + -7)
3[z + (-8 + -3z) + 6] = 3(z + -7)

Reorder the terms:
3[-8 + 6 + z + -3z] = 3(z + -7)

Combine like terms: -8 + 6 = -2
3[-2 + z + -3z] = 3(z + -7)

Combine like terms: z + -3z = -2z
3[-2 + -2z] = 3(z + -7)
[-2 * 3 + -2z * 3] = 3(z + -7)
[-6 + -6z] = 3(z + -7)

Reorder the terms:
-6 + -6z = 3(-7 + z)
-6 + -6z = (-7 * 3 + z * 3)
-6 + -6z = (-21 + 3z)

Solving
-6 + -6z = -21 + 3z

Solving for variable 'z'.

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

Add '-3z' to each side of the equation.
-6 + -6z + -3z = -21 + 3z + -3z

Combine like terms: -6z + -3z = -9z
-6 + -9z = -21 + 3z + -3z

Combine like terms: 3z + -3z = 0
-6 + -9z = -21 + 0
-6 + -9z = -21

Add '6' to each side of the equation.
-6 + 6 + -9z = -21 + 6

Combine like terms: -6 + 6 = 0
0 + -9z = -21 + 6
-9z = -21 + 6

Combine like terms: -21 + 6 = -15
-9z = -15

Divide each side by '-9'.
z = 1.666666667

Simplifying
z = 1.666666667