-20z-5z^2-24=-z^2

Solution for -20z-5z^2-24=-z^2 equation:

Simplifying
-20z + -5z2 + -24 = -1z2

Reorder the terms:
-24 + -20z + -5z2 = -1z2

Solving
-24 + -20z + -5z2 = -1z2

Solving for variable 'z'.

Combine like terms: -5z2 + z2 = -4z2
-24 + -20z + -4z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-24 + -20z + -4z2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(6 + 5z + z2) = 0

Factor a trinomial.
-4((3 + z)(2 + z)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

Solving
3 + z = 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 + z = 0 + -3

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

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

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