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

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


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

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

Multiply (-4 + 3z) * (7 + z)
(-4(7 + z) + 3z * (7 + z)) = 0
((7 * -4 + z * -4) + 3z * (7 + z)) = 0
((-28 + -4z) + 3z * (7 + z)) = 0
(-28 + -4z + (7 * 3z + z * 3z)) = 0
(-28 + -4z + (21z + 3z2)) = 0

Combine like terms: -4z + 21z = 17z
(-28 + 17z + 3z2) = 0

Solving
-28 + 17z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-7 + -1z)(4 + -3z) = 0


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

Simplifying
-7 + -1z = 0

Solving
-7 + -1z = 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 + -1z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1z = 0 + 7
-1z = 0 + 7

Combine like terms: 0 + 7 = 7
-1z = 7

Divide each side by '-1'.
z = -7

Simplifying
z = -7

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

Simplifying
4 + -3z = 0

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

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

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

Divide each side by '-3'.
z = 1.333333333

Simplifying
z = 1.333333333
Solution
z = {-7, 1.333333333}

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