(7+z)(4z+6)=0

Solution for (7+z)(4z+6)=0 equation:

Simplifying
(7 + z)(4z + 6) = 0

Reorder the terms:
(7 + z)(6 + 4z) = 0

Multiply (7 + z) * (6 + 4z)
(7(6 + 4z) + z(6 + 4z)) = 0
((6 * 7 + 4z * 7) + z(6 + 4z)) = 0
((42 + 28z) + z(6 + 4z)) = 0
(42 + 28z + (6 * z + 4z * z)) = 0
(42 + 28z + (6z + 4z2)) = 0

Combine like terms: 28z + 6z = 34z
(42 + 34z + 4z2) = 0

Solving
42 + 34z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 17z + 2z2) = 0

Factor a trinomial.
2((7 + z)(3 + 2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 0

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

Add '-7' to each side of the equation.
7 + -7 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7
Subproblem 2
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
Solution
z = {-7, -1.5}