2z^2+3z-35=0

Solution for 2z^2+3z-35=0 equation:

Simplifying
2z2 + 3z + -35 = 0

Reorder the terms:
-35 + 3z + 2z2 = 0

Solving
-35 + 3z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(7 + -2z) = 0

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
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 = {-5, 3.5}