4z(5z+1)=15z+3

Solution for 4z(5z+1)=15z+3 equation:

Simplifying
4z(5z + 1) = 15z + 3

Reorder the terms:
4z(1 + 5z) = 15z + 3
(1 * 4z + 5z * 4z) = 15z + 3
(4z + 20z2) = 15z + 3

Reorder the terms:
4z + 20z2 = 3 + 15z

Solving
4z + 20z2 = 3 + 15z

Solving for variable 'z'.

Reorder the terms:
-3 + 4z + -15z + 20z2 = 3 + 15z + -3 + -15z

Combine like terms: 4z + -15z = -11z
-3 + -11z + 20z2 = 3 + 15z + -3 + -15z

Reorder the terms:
-3 + -11z + 20z2 = 3 + -3 + 15z + -15z

Combine like terms: 3 + -3 = 0
-3 + -11z + 20z2 = 0 + 15z + -15z
-3 + -11z + 20z2 = 15z + -15z

Combine like terms: 15z + -15z = 0
-3 + -11z + 20z2 = 0

Factor a trinomial.
(-1 + -5z)(3 + -4z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 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 + -4z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4z = 0 + -3
-4z = 0 + -3

Combine like terms: 0 + -3 = -3
-4z = -3

Divide each side by '-4'.
z = 0.75

Simplifying
z = 0.75
Solution
z = {-0.2, 0.75}