z^2+7z-35=-35

Solution for z^2+7z-35=-35 equation:

Simplifying
z2 + 7z + -35 = -35

Reorder the terms:
-35 + 7z + z2 = -35

Add '35' to each side of the equation.
-35 + 7z + 35 + z2 = -35 + 35

Reorder the terms:
-35 + 35 + 7z + z2 = -35 + 35

Combine like terms: -35 + 35 = 0
0 + 7z + z2 = -35 + 35
7z + z2 = -35 + 35

Combine like terms: -35 + 35 = 0
7z + z2 = 0

Solving
7z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

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

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

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

Simplifying
z = -7
Solution
z = {0, -7}