3z^2-12z+9=9z^2-18z+9

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Solution for 3z^2-12z+9=9z^2-18z+9 equation: 


Simplifying
3z2 + -12z + 9 = 9z2 + -18z + 9

Reorder the terms:
9 + -12z + 3z2 = 9z2 + -18z + 9

Reorder the terms:
9 + -12z + 3z2 = 9 + -18z + 9z2

Add '-9' to each side of the equation.
9 + -12z + -9 + 3z2 = 9 + -18z + -9 + 9z2

Reorder the terms:
9 + -9 + -12z + 3z2 = 9 + -18z + -9 + 9z2

Combine like terms: 9 + -9 = 0
0 + -12z + 3z2 = 9 + -18z + -9 + 9z2
-12z + 3z2 = 9 + -18z + -9 + 9z2

Reorder the terms:
-12z + 3z2 = 9 + -9 + -18z + 9z2

Combine like terms: 9 + -9 = 0
-12z + 3z2 = 0 + -18z + 9z2
-12z + 3z2 = -18z + 9z2

Solving
-12z + 3z2 = -18z + 9z2

Solving for variable 'z'.

Reorder the terms:
-12z + 18z + 3z2 + -9z2 = -18z + 9z2 + 18z + -9z2

Combine like terms: -12z + 18z = 6z
6z + 3z2 + -9z2 = -18z + 9z2 + 18z + -9z2

Combine like terms: 3z2 + -9z2 = -6z2
6z + -6z2 = -18z + 9z2 + 18z + -9z2

Reorder the terms:
6z + -6z2 = -18z + 18z + 9z2 + -9z2

Combine like terms: -18z + 18z = 0
6z + -6z2 = 0 + 9z2 + -9z2
6z + -6z2 = 9z2 + -9z2

Combine like terms: 9z2 + -9z2 = 0
6z + -6z2 = 0

Factor out the Greatest Common Factor (GCF), '6z'.
6z(1 + -1z) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

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 = {0, 1}

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