5z^2-29z-42=0

Solution for 5z^2-29z-42=0 equation:

Simplifying
5z2 + -29z + -42 = 0

Reorder the terms:
-42 + -29z + 5z2 = 0

Solving
-42 + -29z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -5z)(7 + -1z) = 0

Subproblem 1
Set the factor '(-6 + -5z)' equal to zero and attempt to solve:

Simplifying
-6 + -5z = 0

Solving
-6 + -5z = 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 + -5z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5z = 0 + 6
-5z = 0 + 6

Combine like terms: 0 + 6 = 6
-5z = 6

Divide each side by '-5'.
z = -1.2

Simplifying
z = -1.2
Subproblem 2
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
Solution
z = {-1.2, 7}