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

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

Simplifying
5z(2z + 3) = 2z + 3

Reorder the terms:
5z(3 + 2z) = 2z + 3
(3 * 5z + 2z * 5z) = 2z + 3
(15z + 10z2) = 2z + 3

Reorder the terms:
15z + 10z2 = 3 + 2z

Solving
15z + 10z2 = 3 + 2z

Solving for variable 'z'.

Reorder the terms:
-3 + 15z + -2z + 10z2 = 3 + 2z + -3 + -2z

Combine like terms: 15z + -2z = 13z
-3 + 13z + 10z2 = 3 + 2z + -3 + -2z

Reorder the terms:
-3 + 13z + 10z2 = 3 + -3 + 2z + -2z

Combine like terms: 3 + -3 = 0
-3 + 13z + 10z2 = 0 + 2z + -2z
-3 + 13z + 10z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
-3 + 13z + 10z2 = 0

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

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

Simplifying
-3 + -2z = 0

Solving
-3 + -2z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2z = 0 + 3
-2z = 0 + 3

Combine like terms: 0 + 3 = 3
-2z = 3

Divide each side by '-2'.
z = -1.5

Simplifying
z = -1.5
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 = {-1.5, 0.2}