(5z+1)(z+3)=-2(5z+1)

Solution for (5z+1)(z+3)=-2(5z+1) equation:

Simplifying
(5z + 1)(z + 3) = -2(5z + 1)

Reorder the terms:
(1 + 5z)(z + 3) = -2(5z + 1)

Reorder the terms:
(1 + 5z)(3 + z) = -2(5z + 1)

Multiply (1 + 5z) * (3 + z)
(1(3 + z) + 5z * (3 + z)) = -2(5z + 1)
((3 * 1 + z * 1) + 5z * (3 + z)) = -2(5z + 1)
((3 + 1z) + 5z * (3 + z)) = -2(5z + 1)
(3 + 1z + (3 * 5z + z * 5z)) = -2(5z + 1)
(3 + 1z + (15z + 5z2)) = -2(5z + 1)

Combine like terms: 1z + 15z = 16z
(3 + 16z + 5z2) = -2(5z + 1)

Reorder the terms:
3 + 16z + 5z2 = -2(1 + 5z)
3 + 16z + 5z2 = (1 * -2 + 5z * -2)
3 + 16z + 5z2 = (-2 + -10z)

Solving
3 + 16z + 5z2 = -2 + -10z

Solving for variable 'z'.

Reorder the terms:
3 + 2 + 16z + 10z + 5z2 = -2 + -10z + 2 + 10z

Combine like terms: 3 + 2 = 5
5 + 16z + 10z + 5z2 = -2 + -10z + 2 + 10z

Combine like terms: 16z + 10z = 26z
5 + 26z + 5z2 = -2 + -10z + 2 + 10z

Reorder the terms:
5 + 26z + 5z2 = -2 + 2 + -10z + 10z

Combine like terms: -2 + 2 = 0
5 + 26z + 5z2 = 0 + -10z + 10z
5 + 26z + 5z2 = -10z + 10z

Combine like terms: -10z + 10z = 0
5 + 26z + 5z2 = 0

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

Subproblem 1
Set the factor '(5 + z)' equal to zero and attempt to solve:

Simplifying
5 + z = 0

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

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

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

Simplifying
z = -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 = {-5, -0.2}