21z+11=11+17z-5z^2

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Solution for 21z+11=11+17z-5z^2 equation: 


Simplifying
21z + 11 = 11 + 17z + -5z2

Reorder the terms:
11 + 21z = 11 + 17z + -5z2

Add '-11' to each side of the equation.
11 + -11 + 21z = 11 + 17z + -11 + -5z2

Combine like terms: 11 + -11 = 0
0 + 21z = 11 + 17z + -11 + -5z2
21z = 11 + 17z + -11 + -5z2

Reorder the terms:
21z = 11 + -11 + 17z + -5z2

Combine like terms: 11 + -11 = 0
21z = 0 + 17z + -5z2
21z = 17z + -5z2

Solving
21z = 17z + -5z2

Solving for variable 'z'.

Combine like terms: 21z + -17z = 4z
4z + 5z2 = 17z + -5z2 + -17z + 5z2

Reorder the terms:
4z + 5z2 = 17z + -17z + -5z2 + 5z2

Combine like terms: 17z + -17z = 0
4z + 5z2 = 0 + -5z2 + 5z2
4z + 5z2 = -5z2 + 5z2

Combine like terms: -5z2 + 5z2 = 0
4z + 5z2 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(4 + 5z) = 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 '(4 + 5z)' equal to zero and attempt to solve:

Simplifying
4 + 5z = 0

Solving
4 + 5z = 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 + 5z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5z = 0 + -4
5z = 0 + -4

Combine like terms: 0 + -4 = -4
5z = -4

Divide each side by '5'.
z = -0.8

Simplifying
z = -0.8
Solution
z = {0, -0.8}

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