4z^2+z=9z

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Solution for 4z^2+z=9z equation: 


Simplifying
4z2 + z = 9z

Reorder the terms:
z + 4z2 = 9z

Solving
z + 4z2 = 9z

Solving for variable 'z'.

Reorder the terms:
z + -9z + 4z2 = 9z + -9z

Combine like terms: z + -9z = -8z
-8z + 4z2 = 9z + -9z

Combine like terms: 9z + -9z = 0
-8z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-2 + z) = 0

Ignore the factor 4.

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 '(-2 + z)' equal to zero and attempt to solve:

Simplifying
-2 + z = 0

Solving
-2 + z = 0

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

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

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

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

Simplifying
z = 2
Solution
z = {0, 2}

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