5(2z-1)4(z+5)=2(z+1)

Solution for 5(2z-1)4(z+5)=2(z+1) equation:

Simplifying
5(2z + -1) * 4(z + 5) = 2(z + 1)

Reorder the terms:
5(-1 + 2z) * 4(z + 5) = 2(z + 1)

Reorder the terms:
5(-1 + 2z) * 4(5 + z) = 2(z + 1)

Reorder the terms for easier multiplication:
5 * 4(-1 + 2z)(5 + z) = 2(z + 1)

Multiply 5 * 4
20(-1 + 2z)(5 + z) = 2(z + 1)

Multiply (-1 + 2z) * (5 + z)
20(-1(5 + z) + 2z * (5 + z)) = 2(z + 1)
20((5 * -1 + z * -1) + 2z * (5 + z)) = 2(z + 1)
20((-5 + -1z) + 2z * (5 + z)) = 2(z + 1)
20(-5 + -1z + (5 * 2z + z * 2z)) = 2(z + 1)
20(-5 + -1z + (10z + 2z2)) = 2(z + 1)

Combine like terms: -1z + 10z = 9z
20(-5 + 9z + 2z2) = 2(z + 1)
(-5 * 20 + 9z * 20 + 2z2 * 20) = 2(z + 1)
(-100 + 180z + 40z2) = 2(z + 1)

Reorder the terms:
-100 + 180z + 40z2 = 2(1 + z)
-100 + 180z + 40z2 = (1 * 2 + z * 2)
-100 + 180z + 40z2 = (2 + 2z)

Solving
-100 + 180z + 40z2 = 2 + 2z

Solving for variable 'z'.

Reorder the terms:
-100 + -2 + 180z + -2z + 40z2 = 2 + 2z + -2 + -2z

Combine like terms: -100 + -2 = -102
-102 + 180z + -2z + 40z2 = 2 + 2z + -2 + -2z

Combine like terms: 180z + -2z = 178z
-102 + 178z + 40z2 = 2 + 2z + -2 + -2z

Reorder the terms:
-102 + 178z + 40z2 = 2 + -2 + 2z + -2z

Combine like terms: 2 + -2 = 0
-102 + 178z + 40z2 = 0 + 2z + -2z
-102 + 178z + 40z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
-102 + 178z + 40z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-51 + 89z + 20z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-51 + 89z + 20z2)' equal to zero and attempt to solve:

Simplifying
-51 + 89z + 20z2 = 0

Solving
-51 + 89z + 20z2 = 0

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

Divide each side by '20'.
-2.55 + 4.45z + z2 = 0.0

Move the constant term to the right:

Add '2.55' to each side of the equation.
-2.55 + 4.45z + 2.55 + z2 = 0.0 + 2.55

Reorder the terms:
-2.55 + 2.55 + 4.45z + z2 = 0.0 + 2.55

Combine like terms: -2.55 + 2.55 = 0.00
0.00 + 4.45z + z2 = 0.0 + 2.55
4.45z + z2 = 0.0 + 2.55

Combine like terms: 0.0 + 2.55 = 2.55
4.45z + z2 = 2.55

The z term is 4.45z.  Take half its coefficient (2.225).
Square it (4.950625) and add it to both sides.

Add '4.950625' to each side of the equation.
4.45z + 4.950625 + z2 = 2.55 + 4.950625

Reorder the terms:
4.950625 + 4.45z + z2 = 2.55 + 4.950625

Combine like terms: 2.55 + 4.950625 = 7.500625
4.950625 + 4.45z + z2 = 7.500625

Factor a perfect square on the left side:
(z + 2.225)(z + 2.225) = 7.500625

Calculate the square root of the right side: 2.738726894

Break this problem into two subproblems by setting 
(z + 2.225) equal to 2.738726894 and -2.738726894.

Subproblem 1
z + 2.225 = 2.738726894

Simplifying
z + 2.225 = 2.738726894

Reorder the terms:
2.225 + z = 2.738726894

Solving
2.225 + z = 2.738726894

Solving for variable 'z'.

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

Add '-2.225' to each side of the equation.
2.225 + -2.225 + z = 2.738726894 + -2.225

Combine like terms: 2.225 + -2.225 = 0.000
0.000 + z = 2.738726894 + -2.225
z = 2.738726894 + -2.225

Combine like terms: 2.738726894 + -2.225 = 0.513726894
z = 0.513726894

Simplifying
z = 0.513726894

Subproblem 2
z + 2.225 = -2.738726894

Simplifying
z + 2.225 = -2.738726894

Reorder the terms:
2.225 + z = -2.738726894

Solving
2.225 + z = -2.738726894

Solving for variable 'z'.

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

Add '-2.225' to each side of the equation.
2.225 + -2.225 + z = -2.738726894 + -2.225

Combine like terms: 2.225 + -2.225 = 0.000
0.000 + z = -2.738726894 + -2.225
z = -2.738726894 + -2.225

Combine like terms: -2.738726894 + -2.225 = -4.963726894
z = -4.963726894

Simplifying
z = -4.963726894

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.513726894, -4.963726894}
Solution
z = {0.513726894, -4.963726894}