3z+7z=33z-8(2-6)+z(8888z-7999z)

Solution for 3z+7z=33z-8(2-6)+z(8888z-7999z) equation:

Simplifying
3z + 7z = 33z + -8(2 + -6) + z(8888z + -7999z)

Combine like terms: 3z + 7z = 10z
10z = 33z + -8(2 + -6) + z(8888z + -7999z)

Combine like terms: 2 + -6 = -4
10z = 33z + -8(-4) + z(8888z + -7999z)

Multiply -8 * -4
10z = 33z + 32 + z(8888z + -7999z)

Combine like terms: 8888z + -7999z = 889z
10z = 33z + 32 + z(889z)

Remove parenthesis around (889z)
10z = 33z + 32 + z * 889z

Reorder the terms for easier multiplication:
10z = 33z + 32 + 889z * z

Multiply z * z
10z = 33z + 32 + 889z2

Reorder the terms:
10z = 32 + 33z + 889z2

Solving
10z = 32 + 33z + 889z2

Solving for variable 'z'.

Reorder the terms:
-32 + 10z + -33z + -889z2 = 32 + 33z + 889z2 + -32 + -33z + -889z2

Combine like terms: 10z + -33z = -23z
-32 + -23z + -889z2 = 32 + 33z + 889z2 + -32 + -33z + -889z2

Reorder the terms:
-32 + -23z + -889z2 = 32 + -32 + 33z + -33z + 889z2 + -889z2

Combine like terms: 32 + -32 = 0
-32 + -23z + -889z2 = 0 + 33z + -33z + 889z2 + -889z2
-32 + -23z + -889z2 = 33z + -33z + 889z2 + -889z2

Combine like terms: 33z + -33z = 0
-32 + -23z + -889z2 = 0 + 889z2 + -889z2
-32 + -23z + -889z2 = 889z2 + -889z2

Combine like terms: 889z2 + -889z2 = 0
-32 + -23z + -889z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 23z + 889z2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(32 + 23z + 889z2)' equal to zero and attempt to solve:

Simplifying
32 + 23z + 889z2 = 0

Solving
32 + 23z + 889z2 = 0

Begin completing the square.  Divide all terms by
889 the coefficient of the squared term: 

Divide each side by '889'.
0.03599550056 + 0.02587176603z + z2 = 0

Move the constant term to the right:

Add '-0.03599550056' to each side of the equation.
0.03599550056 + 0.02587176603z + -0.03599550056 + z2 = 0 + -0.03599550056

Reorder the terms:
0.03599550056 + -0.03599550056 + 0.02587176603z + z2 = 0 + -0.03599550056

Combine like terms: 0.03599550056 + -0.03599550056 = 0.00000000000
0.00000000000 + 0.02587176603z + z2 = 0 + -0.03599550056
0.02587176603z + z2 = 0 + -0.03599550056

Combine like terms: 0 + -0.03599550056 = -0.03599550056
0.02587176603z + z2 = -0.03599550056

The z term is 0.02587176603z.  Take half its coefficient (0.01293588302).
Square it (0.0001673370695) and add it to both sides.

Add '0.0001673370695' to each side of the equation.
0.02587176603z + 0.0001673370695 + z2 = -0.03599550056 + 0.0001673370695

Reorder the terms:
0.0001673370695 + 0.02587176603z + z2 = -0.03599550056 + 0.0001673370695

Combine like terms: -0.03599550056 + 0.0001673370695 = -0.0358281634905
0.0001673370695 + 0.02587176603z + z2 = -0.0358281634905

Factor a perfect square on the left side:
(z + 0.01293588302)(z + 0.01293588302) = -0.0358281634905

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.