(3z-7)(z+12)=0

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Solution for (3z-7)(z+12)=0 equation: 


Simplifying
(3z + -7)(z + 12) = 0

Reorder the terms:
(-7 + 3z)(z + 12) = 0

Reorder the terms:
(-7 + 3z)(12 + z) = 0

Multiply (-7 + 3z) * (12 + z)
(-7(12 + z) + 3z * (12 + z)) = 0
((12 * -7 + z * -7) + 3z * (12 + z)) = 0
((-84 + -7z) + 3z * (12 + z)) = 0
(-84 + -7z + (12 * 3z + z * 3z)) = 0
(-84 + -7z + (36z + 3z2)) = 0

Combine like terms: -7z + 36z = 29z
(-84 + 29z + 3z2) = 0

Solving
-84 + 29z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-12 + -1z)(7 + -3z) = 0


Subproblem 1
Set the factor '(-12 + -1z)' equal to zero and attempt to solve:

Simplifying
-12 + -1z = 0

Solving
-12 + -1z = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1z = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1z = 0 + 12
-1z = 0 + 12

Combine like terms: 0 + 12 = 12
-1z = 12

Divide each side by '-1'.
z = -12

Simplifying
z = -12

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 = {-12, 2.333333333}

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