(4+z)(3z+7)=0

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Solution for (4+z)(3z+7)=0 equation: 


Simplifying
(4 + z)(3z + 7) = 0

Reorder the terms:
(4 + z)(7 + 3z) = 0

Multiply (4 + z) * (7 + 3z)
(4(7 + 3z) + z(7 + 3z)) = 0
((7 * 4 + 3z * 4) + z(7 + 3z)) = 0
((28 + 12z) + z(7 + 3z)) = 0
(28 + 12z + (7 * z + 3z * z)) = 0
(28 + 12z + (7z + 3z2)) = 0

Combine like terms: 12z + 7z = 19z
(28 + 19z + 3z2) = 0

Solving
28 + 19z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(7 + 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 '(7 + 3z)' equal to zero and attempt to solve:

Simplifying
7 + 3z = 0

Solving
7 + 3z = 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 + 3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3z = 0 + -7
3z = 0 + -7

Combine like terms: 0 + -7 = -7
3z = -7

Divide each side by '3'.
z = -2.333333333

Simplifying
z = -2.333333333
Solution
z = {-4, -2.333333333}

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