-z^2-3z+70=0

Solution for -z^2-3z+70=0 equation:

Simplifying
-1z2 + -3z + 70 = 0

Reorder the terms:
70 + -3z + -1z2 = 0

Solving
70 + -3z + -1z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(7 + -1z)(10 + z) = 0

Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 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 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Subproblem 2
Set the factor '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 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 + z = 0 + -10

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

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

Simplifying
z = -10
Solution
z = {7, -10}