8z(-4z-7)+8z=-16z

Solution for 8z(-4z-7)+8z=-16z equation:

Simplifying
8z(-4z + -7) + 8z = -16z

Reorder the terms:
8z(-7 + -4z) + 8z = -16z
(-7 * 8z + -4z * 8z) + 8z = -16z
(-56z + -32z2) + 8z = -16z

Reorder the terms:
-56z + 8z + -32z2 = -16z

Combine like terms: -56z + 8z = -48z
-48z + -32z2 = -16z

Solving
-48z + -32z2 = -16z

Solving for variable 'z'.

Reorder the terms:
-48z + 16z + -32z2 = -16z + 16z

Combine like terms: -48z + 16z = -32z
-32z + -32z2 = -16z + 16z

Combine like terms: -16z + 16z = 0
-32z + -32z2 = 0

Factor out the Greatest Common Factor (GCF), '-32z'.
-32z(1 + z) = 0

Ignore the factor -32.
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 '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {0, -1}