5z^2+37z+42=0

Solution for 5z^2+37z+42=0 equation:

Simplifying
5z2 + 37z + 42 = 0

Reorder the terms:
42 + 37z + 5z2 = 0

Solving
42 + 37z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + z)(7 + 5z) = 0

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 0

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

Add '-6' to each side of the equation.
6 + -6 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(7 + 5z)' equal to zero and attempt to solve:

Simplifying
7 + 5z = 0

Solving
7 + 5z = 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 + 5z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5z = 0 + -7
5z = 0 + -7

Combine like terms: 0 + -7 = -7
5z = -7

Divide each side by '5'.
z = -1.4

Simplifying
z = -1.4
Solution
z = {-6, -1.4}