5z(3z+1)=3z+1

Solution for 5z(3z+1)=3z+1 equation:

Simplifying
5z(3z + 1) = 3z + 1

Reorder the terms:
5z(1 + 3z) = 3z + 1
(1 * 5z + 3z * 5z) = 3z + 1
(5z + 15z2) = 3z + 1

Reorder the terms:
5z + 15z2 = 1 + 3z

Solving
5z + 15z2 = 1 + 3z

Solving for variable 'z'.

Reorder the terms:
-1 + 5z + -3z + 15z2 = 1 + 3z + -1 + -3z

Combine like terms: 5z + -3z = 2z
-1 + 2z + 15z2 = 1 + 3z + -1 + -3z

Reorder the terms:
-1 + 2z + 15z2 = 1 + -1 + 3z + -3z

Combine like terms: 1 + -1 = 0
-1 + 2z + 15z2 = 0 + 3z + -3z
-1 + 2z + 15z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
-1 + 2z + 15z2 = 0

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

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 '(1 + -5z)' equal to zero and attempt to solve:

Simplifying
1 + -5z = 0

Solving
1 + -5z = 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 + -5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5z = 0 + -1
-5z = 0 + -1

Combine like terms: 0 + -1 = -1
-5z = -1

Divide each side by '-5'.
z = 0.2

Simplifying
z = 0.2
Solution
z = {-0.3333333333, 0.2}