2(z+5)=3(2-2z)8z

Solution for 2(z+5)=3(2-2z)8z equation:

Simplifying
2(z + 5) = 3(2 + -2z) * 8z

Reorder the terms:
2(5 + z) = 3(2 + -2z) * 8z
(5 * 2 + z * 2) = 3(2 + -2z) * 8z
(10 + 2z) = 3(2 + -2z) * 8z

Reorder the terms for easier multiplication:
10 + 2z = 3 * 8z(2 + -2z)

Multiply 3 * 8
10 + 2z = 24z(2 + -2z)
10 + 2z = (2 * 24z + -2z * 24z)
10 + 2z = (48z + -48z2)

Solving
10 + 2z = 48z + -48z2

Solving for variable 'z'.

Combine like terms: 2z + -48z = -46z
10 + -46z + 48z2 = 48z + -48z2 + -48z + 48z2

Reorder the terms:
10 + -46z + 48z2 = 48z + -48z + -48z2 + 48z2

Combine like terms: 48z + -48z = 0
10 + -46z + 48z2 = 0 + -48z2 + 48z2
10 + -46z + 48z2 = -48z2 + 48z2

Combine like terms: -48z2 + 48z2 = 0
10 + -46z + 48z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -23z + 24z2) = 0

Factor a trinomial.
2((1 + -3z)(5 + -8z)) = 0

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

Simplifying
1 + -3z = 0

Solving
1 + -3z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Subproblem 2
Set the factor '(5 + -8z)' equal to zero and attempt to solve:

Simplifying
5 + -8z = 0

Solving
5 + -8z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8z = 0 + -5
-8z = 0 + -5

Combine like terms: 0 + -5 = -5
-8z = -5

Divide each side by '-8'.
z = 0.625

Simplifying
z = 0.625
Solution
z = {0.3333333333, 0.625}