7z^2+42z+56=0

Solution for 7z^2+42z+56=0 equation:

Simplifying
7z2 + 42z + 56 = 0

Reorder the terms:
56 + 42z + 7z2 = 0

Solving
56 + 42z + 7z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7'.
7(8 + 6z + z2) = 0

Factor a trinomial.
7((4 + z)(2 + z)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 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 + z = 0 + -2

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

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

Simplifying
z = -2
Solution
z = {-4, -2}