2z^2-13z=-21

Solution for 2z^2-13z=-21 equation:

Simplifying
2z2 + -13z = -21

Reorder the terms:
-13z + 2z2 = -21

Solving
-13z + 2z2 = -21

Solving for variable 'z'.

Reorder the terms:
21 + -13z + 2z2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + -13z + 2z2 = 0

Factor a trinomial.
(3 + -1z)(7 + -2z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(7 + -2z)' equal to zero and attempt to solve:

Simplifying
7 + -2z = 0

Solving
7 + -2z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2z = 0 + -7
-2z = 0 + -7

Combine like terms: 0 + -7 = -7
-2z = -7

Divide each side by '-2'.
z = 3.5

Simplifying
z = 3.5
Solution
z = {3, 3.5}