2z(z+9)=2z+18z-4

Solution for 2z(z+9)=2z+18z-4 equation:

Simplifying
2z(z + 9) = 2z + 18z + -4

Reorder the terms:
2z(9 + z) = 2z + 18z + -4
(9 * 2z + z * 2z) = 2z + 18z + -4
(18z + 2z2) = 2z + 18z + -4

Reorder the terms:
18z + 2z2 = -4 + 2z + 18z

Combine like terms: 2z + 18z = 20z
18z + 2z2 = -4 + 20z

Solving
18z + 2z2 = -4 + 20z

Solving for variable 'z'.

Reorder the terms:
4 + 18z + -20z + 2z2 = -4 + 20z + 4 + -20z

Combine like terms: 18z + -20z = -2z
4 + -2z + 2z2 = -4 + 20z + 4 + -20z

Reorder the terms:
4 + -2z + 2z2 = -4 + 4 + 20z + -20z

Combine like terms: -4 + 4 = 0
4 + -2z + 2z2 = 0 + 20z + -20z
4 + -2z + 2z2 = 20z + -20z

Combine like terms: 20z + -20z = 0
4 + -2z + 2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -1z + z2)' equal to zero and attempt to solve:

Simplifying
2 + -1z + z2 = 0

Solving
2 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -1z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z + z2 = 0 + -2
-1z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1z + z2 = -2

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -2 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1z + z2 = -1.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.