-4z(z-1)(z+7)=0

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Solution for -4z(z-1)(z+7)=0 equation: 


Simplifying
-4z(z + -1)(z + 7) = 0

Reorder the terms:
-4z(-1 + z)(z + 7) = 0

Reorder the terms:
-4z(-1 + z)(7 + z) = 0

Multiply (-1 + z) * (7 + z)
-4z(-1(7 + z) + z(7 + z)) = 0
-4z((7 * -1 + z * -1) + z(7 + z)) = 0
-4z((-7 + -1z) + z(7 + z)) = 0
-4z(-7 + -1z + (7 * z + z * z)) = 0
-4z(-7 + -1z + (7z + z2)) = 0

Combine like terms: -1z + 7z = 6z
-4z(-7 + 6z + z2) = 0
(-7 * -4z + 6z * -4z + z2 * -4z) = 0
(28z + -24z2 + -4z3) = 0

Solving
28z + -24z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(7 + -6z + -1z2) = 0

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1

Subproblem 3
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 = {0, 1, -7}

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