3(z+7)(-z+2)=0

Solution for 3(z+7)(-z+2)=0 equation:

Simplifying
3(z + 7)(-1z + 2) = 0

Reorder the terms:
3(7 + z)(-1z + 2) = 0

Reorder the terms:
3(7 + z)(2 + -1z) = 0

Multiply (7 + z) * (2 + -1z)
3(7(2 + -1z) + z(2 + -1z)) = 0
3((2 * 7 + -1z * 7) + z(2 + -1z)) = 0
3((14 + -7z) + z(2 + -1z)) = 0
3(14 + -7z + (2 * z + -1z * z)) = 0
3(14 + -7z + (2z + -1z2)) = 0

Combine like terms: -7z + 2z = -5z
3(14 + -5z + -1z2) = 0
(14 * 3 + -5z * 3 + -1z2 * 3) = 0
(42 + -15z + -3z2) = 0

Solving
42 + -15z + -3z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -5z + -1z2) = 0

Factor a trinomial.
3((2 + -1z)(7 + z)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

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