(3z+5)(z+3)=7

Solution for (3z+5)(z+3)=7 equation:

Simplifying
(3z + 5)(z + 3) = 7

Reorder the terms:
(5 + 3z)(z + 3) = 7

Reorder the terms:
(5 + 3z)(3 + z) = 7

Multiply (5 + 3z) * (3 + z)
(5(3 + z) + 3z * (3 + z)) = 7
((3 * 5 + z * 5) + 3z * (3 + z)) = 7
((15 + 5z) + 3z * (3 + z)) = 7
(15 + 5z + (3 * 3z + z * 3z)) = 7
(15 + 5z + (9z + 3z2)) = 7

Combine like terms: 5z + 9z = 14z
(15 + 14z + 3z2) = 7

Solving
15 + 14z + 3z2 = 7

Solving for variable 'z'.

Reorder the terms:
15 + -7 + 14z + 3z2 = 7 + -7

Combine like terms: 15 + -7 = 8
8 + 14z + 3z2 = 7 + -7

Combine like terms: 7 + -7 = 0
8 + 14z + 3z2 = 0

Factor a trinomial.
(4 + z)(2 + 3z) = 0

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

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

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

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

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

Simplifying
2 + 3z = 0

Solving
2 + 3z = 0

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

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

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

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

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Solution
z = {-4, -0.6666666667}