-4z(z+2)(z-7)=0

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Solution for -4z(z+2)(z-7)=0 equation: 


Simplifying
-4z(z + 2)(z + -7) = 0

Reorder the terms:
-4z(2 + z)(z + -7) = 0

Reorder the terms:
-4z(2 + z)(-7 + z) = 0

Multiply (2 + z) * (-7 + z)
-4z(2(-7 + z) + z(-7 + z)) = 0
-4z((-7 * 2 + z * 2) + z(-7 + z)) = 0
-4z((-14 + 2z) + z(-7 + z)) = 0
-4z(-14 + 2z + (-7 * z + z * z)) = 0
-4z(-14 + 2z + (-7z + z2)) = 0

Combine like terms: 2z + -7z = -5z
-4z(-14 + -5z + z2) = 0
(-14 * -4z + -5z * -4z + z2 * -4z) = 0
(56z + 20z2 + -4z3) = 0

Solving
56z + 20z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(14 + 5z + -1z2) = 0

Factor a trinomial.
4z((7 + -1z)(2 + z)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0

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

Simplifying
2 + z = 0

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

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

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

Simplifying
z = -2
Solution
z = {0, 7, -2}

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