8z^2-3z+6-(10z^2+3z-8)=

Solution for 8z^2-3z+6-(10z^2+3z-8)= equation:

Simplifying
8z2 + -3z + 6 + -1(10z2 + 3z + -8) = 0

Reorder the terms:
8z2 + -3z + 6 + -1(-8 + 3z + 10z2) = 0
8z2 + -3z + 6 + (-8 * -1 + 3z * -1 + 10z2 * -1) = 0
8z2 + -3z + 6 + (8 + -3z + -10z2) = 0

Reorder the terms:
6 + 8 + -3z + -3z + 8z2 + -10z2 = 0

Combine like terms: 6 + 8 = 14
14 + -3z + -3z + 8z2 + -10z2 = 0

Combine like terms: -3z + -3z = -6z
14 + -6z + 8z2 + -10z2 = 0

Combine like terms: 8z2 + -10z2 = -2z2
14 + -6z + -2z2 = 0

Solving
14 + -6z + -2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -3z + -1z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -3z + -1z2)' equal to zero and attempt to solve:

Simplifying
7 + -3z + -1z2 = 0

Solving
7 + -3z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + 3z + z2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 3z + 7 + z2 = 0 + 7

Reorder the terms:
-7 + 7 + 3z + z2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3z + z2 = 0 + 7
3z + z2 = 0 + 7

Combine like terms: 0 + 7 = 7
3z + z2 = 7

The z term is 3z.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3z + 2.25 + z2 = 7 + 2.25

Reorder the terms:
2.25 + 3z + z2 = 7 + 2.25

Combine like terms: 7 + 2.25 = 9.25
2.25 + 3z + z2 = 9.25

Factor a perfect square on the left side:
(z + 1.5)(z + 1.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(z + 1.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
z + 1.5 = 3.041381265

Simplifying
z + 1.5 = 3.041381265

Reorder the terms:
1.5 + z = 3.041381265

Solving
1.5 + z = 3.041381265

Solving for variable 'z'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + z = 3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + z = 3.041381265 + -1.5
z = 3.041381265 + -1.5

Combine like terms: 3.041381265 + -1.5 = 1.541381265
z = 1.541381265

Simplifying
z = 1.541381265

Subproblem 2
z + 1.5 = -3.041381265

Simplifying
z + 1.5 = -3.041381265

Reorder the terms:
1.5 + z = -3.041381265

Solving
1.5 + z = -3.041381265

Solving for variable 'z'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + z = -3.041381265 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + z = -3.041381265 + -1.5
z = -3.041381265 + -1.5

Combine like terms: -3.041381265 + -1.5 = -4.541381265
z = -4.541381265

Simplifying
z = -4.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {1.541381265, -4.541381265}
Solution
z = {1.541381265, -4.541381265}