2z^2=z+6

Solution for 2z^2=z+6 equation:

Simplifying
2z2 = z + 6

Reorder the terms:
2z2 = 6 + z

Solving
2z2 = 6 + z

Solving for variable 'z'.

Reorder the terms:
-6 + -1z + 2z2 = 6 + z + -6 + -1z

Reorder the terms:
-6 + -1z + 2z2 = 6 + -6 + z + -1z

Combine like terms: 6 + -6 = 0
-6 + -1z + 2z2 = 0 + z + -1z
-6 + -1z + 2z2 = z + -1z

Combine like terms: z + -1z = 0
-6 + -1z + 2z2 = 0

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

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 '(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
Solution
z = {-1.5, 2}