6(3z-1)-z(z+1)=5(z+1)

Solution for 6(3z-1)-z(z+1)=5(z+1) equation:

Simplifying
6(3z + -1) + -1z(z + 1) = 5(z + 1)

Reorder the terms:
6(-1 + 3z) + -1z(z + 1) = 5(z + 1)
(-1 * 6 + 3z * 6) + -1z(z + 1) = 5(z + 1)
(-6 + 18z) + -1z(z + 1) = 5(z + 1)

Reorder the terms:
-6 + 18z + -1z(1 + z) = 5(z + 1)
-6 + 18z + (1 * -1z + z * -1z) = 5(z + 1)
-6 + 18z + (-1z + -1z2) = 5(z + 1)

Combine like terms: 18z + -1z = 17z
-6 + 17z + -1z2 = 5(z + 1)

Reorder the terms:
-6 + 17z + -1z2 = 5(1 + z)
-6 + 17z + -1z2 = (1 * 5 + z * 5)
-6 + 17z + -1z2 = (5 + 5z)

Solving
-6 + 17z + -1z2 = 5 + 5z

Solving for variable 'z'.

Reorder the terms:
-6 + -5 + 17z + -5z + -1z2 = 5 + 5z + -5 + -5z

Combine like terms: -6 + -5 = -11
-11 + 17z + -5z + -1z2 = 5 + 5z + -5 + -5z

Combine like terms: 17z + -5z = 12z
-11 + 12z + -1z2 = 5 + 5z + -5 + -5z

Reorder the terms:
-11 + 12z + -1z2 = 5 + -5 + 5z + -5z

Combine like terms: 5 + -5 = 0
-11 + 12z + -1z2 = 0 + 5z + -5z
-11 + 12z + -1z2 = 5z + -5z

Combine like terms: 5z + -5z = 0
-11 + 12z + -1z2 = 0

Factor a trinomial.
(-11 + z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-11 + z)' equal to zero and attempt to solve:

Simplifying
-11 + z = 0

Solving
-11 + z = 0

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

Add '11' to each side of the equation.
-11 + 11 + z = 0 + 11

Combine like terms: -11 + 11 = 0
0 + z = 0 + 11
z = 0 + 11

Combine like terms: 0 + 11 = 11
z = 11

Simplifying
z = 11
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Solution
z = {11, 1}