4z(z-7)(z+8)=0

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Solution for 4z(z-7)(z+8)=0 equation: 


Simplifying
4z(z + -7)(z + 8) = 0

Reorder the terms:
4z(-7 + z)(z + 8) = 0

Reorder the terms:
4z(-7 + z)(8 + z) = 0

Multiply (-7 + z) * (8 + z)
4z(-7(8 + z) + z(8 + z)) = 0
4z((8 * -7 + z * -7) + z(8 + z)) = 0
4z((-56 + -7z) + z(8 + z)) = 0
4z(-56 + -7z + (8 * z + z * z)) = 0
4z(-56 + -7z + (8z + z2)) = 0

Combine like terms: -7z + 8z = 1z
4z(-56 + 1z + z2) = 0
(-56 * 4z + 1z * 4z + z2 * 4z) = 0
(-224z + 4z2 + 4z3) = 0

Solving
-224z + 4z2 + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(-56 + z + z2) = 0

Factor a trinomial.
4z((-8 + -1z)(7 + -1z)) = 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 '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8

Subproblem 3
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
Solution
z = {0, -8, 7}

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