4(z^2+11z-2)=-2z^2-7z+2

Solution for 4(z^2+11z-2)=-2z^2-7z+2 equation:

Simplifying
4(z2 + 11z + -2) = -2z2 + -7z + 2

Reorder the terms:
4(-2 + 11z + z2) = -2z2 + -7z + 2
(-2 * 4 + 11z * 4 + z2 * 4) = -2z2 + -7z + 2
(-8 + 44z + 4z2) = -2z2 + -7z + 2

Reorder the terms:
-8 + 44z + 4z2 = 2 + -7z + -2z2

Solving
-8 + 44z + 4z2 = 2 + -7z + -2z2

Solving for variable 'z'.

Reorder the terms:
-8 + -2 + 44z + 7z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: -8 + -2 = -10
-10 + 44z + 7z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: 44z + 7z = 51z
-10 + 51z + 4z2 + 2z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Combine like terms: 4z2 + 2z2 = 6z2
-10 + 51z + 6z2 = 2 + -7z + -2z2 + -2 + 7z + 2z2

Reorder the terms:
-10 + 51z + 6z2 = 2 + -2 + -7z + 7z + -2z2 + 2z2

Combine like terms: 2 + -2 = 0
-10 + 51z + 6z2 = 0 + -7z + 7z + -2z2 + 2z2
-10 + 51z + 6z2 = -7z + 7z + -2z2 + 2z2

Combine like terms: -7z + 7z = 0
-10 + 51z + 6z2 = 0 + -2z2 + 2z2
-10 + 51z + 6z2 = -2z2 + 2z2

Combine like terms: -2z2 + 2z2 = 0
-10 + 51z + 6z2 = 0

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

Divide each side by '6'.
-1.666666667 + 8.5z + z2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 8.5z + 1.666666667 + z2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 8.5z + z2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 8.5z + z2 = 0 + 1.666666667
8.5z + z2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
8.5z + z2 = 1.666666667

The z term is 8.5z.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5z + 18.0625 + z2 = 1.666666667 + 18.0625

Reorder the terms:
18.0625 + 8.5z + z2 = 1.666666667 + 18.0625

Combine like terms: 1.666666667 + 18.0625 = 19.729166667
18.0625 + 8.5z + z2 = 19.729166667

Factor a perfect square on the left side:
(z + 4.25)(z + 4.25) = 19.729166667

Calculate the square root of the right side: 4.441752657

Break this problem into two subproblems by setting 
(z + 4.25) equal to 4.441752657 and -4.441752657.

Subproblem 1
z + 4.25 = 4.441752657

Simplifying
z + 4.25 = 4.441752657

Reorder the terms:
4.25 + z = 4.441752657

Solving
4.25 + z = 4.441752657

Solving for variable 'z'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + z = 4.441752657 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + z = 4.441752657 + -4.25
z = 4.441752657 + -4.25

Combine like terms: 4.441752657 + -4.25 = 0.191752657
z = 0.191752657

Simplifying
z = 0.191752657

Subproblem 2
z + 4.25 = -4.441752657

Simplifying
z + 4.25 = -4.441752657

Reorder the terms:
4.25 + z = -4.441752657

Solving
4.25 + z = -4.441752657

Solving for variable 'z'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + z = -4.441752657 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + z = -4.441752657 + -4.25
z = -4.441752657 + -4.25

Combine like terms: -4.441752657 + -4.25 = -8.691752657
z = -8.691752657

Simplifying
z = -8.691752657

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.191752657, -8.691752657}