2z^2-21z+3=39

Solution for 2z^2-21z+3=39 equation:

Simplifying
2z2 + -21z + 3 = 39

Reorder the terms:
3 + -21z + 2z2 = 39

Solving
3 + -21z + 2z2 = 39

Solving for variable 'z'.

Reorder the terms:
3 + -39 + -21z + 2z2 = 39 + -39

Combine like terms: 3 + -39 = -36
-36 + -21z + 2z2 = 39 + -39

Combine like terms: 39 + -39 = 0
-36 + -21z + 2z2 = 0

Factor a trinomial.
(-3 + -2z)(12 + -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 '(12 + -1z)' equal to zero and attempt to solve:

Simplifying
12 + -1z = 0

Solving
12 + -1z = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1z = 0 + -12
-1z = 0 + -12

Combine like terms: 0 + -12 = -12
-1z = -12

Divide each side by '-1'.
z = 12

Simplifying
z = 12
Solution
z = {-1.5, 12}