10z-6=2z(6z-6)

Solution for 10z-6=2z(6z-6) equation:

Simplifying
10z + -6 = 2z(6z + -6)

Reorder the terms:
-6 + 10z = 2z(6z + -6)

Reorder the terms:
-6 + 10z = 2z(-6 + 6z)
-6 + 10z = (-6 * 2z + 6z * 2z)
-6 + 10z = (-12z + 12z2)

Solving
-6 + 10z = -12z + 12z2

Solving for variable 'z'.

Combine like terms: 10z + 12z = 22z
-6 + 22z + -12z2 = -12z + 12z2 + 12z + -12z2

Reorder the terms:
-6 + 22z + -12z2 = -12z + 12z + 12z2 + -12z2

Combine like terms: -12z + 12z = 0
-6 + 22z + -12z2 = 0 + 12z2 + -12z2
-6 + 22z + -12z2 = 12z2 + -12z2

Combine like terms: 12z2 + -12z2 = 0
-6 + 22z + -12z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 11z + -6z2) = 0

Factor a trinomial.
2((-3 + 2z)(1 + -3z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2z)' equal to zero and attempt to solve:

Simplifying
-3 + 2z = 0

Solving
-3 + 2z = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2z = 0 + 3
2z = 0 + 3

Combine like terms: 0 + 3 = 3
2z = 3

Divide each side by '2'.
z = 1.5

Simplifying
z = 1.5
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {1.5, 0.3333333333}