2z^2+19z-10=0

Solution for 2z^2+19z-10=0 equation:

Simplifying
2z2 + 19z + -10 = 0

Reorder the terms:
-10 + 19z + 2z2 = 0

Solving
-10 + 19z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-10 + -1z)(1 + -2z) = 0

Subproblem 1
Set the factor '(-10 + -1z)' equal to zero and attempt to solve:

Simplifying
-10 + -1z = 0

Solving
-10 + -1z = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1z = 0 + 10
-1z = 0 + 10

Combine like terms: 0 + 10 = 10
-1z = 10

Divide each side by '-1'.
z = -10

Simplifying
z = -10
Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

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

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-10, 0.5}