-2z^2+5z+13=6

Solution for -2z^2+5z+13=6 equation:

Simplifying
-2z2 + 5z + 13 = 6

Reorder the terms:
13 + 5z + -2z2 = 6

Solving
13 + 5z + -2z2 = 6

Solving for variable 'z'.

Reorder the terms:
13 + -6 + 5z + -2z2 = 6 + -6

Combine like terms: 13 + -6 = 7
7 + 5z + -2z2 = 6 + -6

Combine like terms: 6 + -6 = 0
7 + 5z + -2z2 = 0

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

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

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {3.5, -1}