2z^2-13z+20=z

Solution for 2z^2-13z+20=z equation:

Simplifying
2z2 + -13z + 20 = z

Reorder the terms:
20 + -13z + 2z2 = z

Solving
20 + -13z + 2z2 = z

Solving for variable 'z'.

Reorder the terms:
20 + -13z + -1z + 2z2 = z + -1z

Combine like terms: -13z + -1z = -14z
20 + -14z + 2z2 = z + -1z

Combine like terms: z + -1z = 0
20 + -14z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7z + z2) = 0

Factor a trinomial.
2((2 + -1z)(5 + -1z)) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {2, 5}