7z^2+7z-42=0

Solution for 7z^2+7z-42=0 equation:

Simplifying
7z2 + 7z + -42 = 0

Reorder the terms:
-42 + 7z + 7z2 = 0

Solving
-42 + 7z + 7z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + z + z2) = 0

Factor a trinomial.
7((-3 + -1z)(2 + -1z)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {-3, 2}