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

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


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

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

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

Multiply (-7 + z) * (-4 + -1z)
4(-7(-4 + -1z) + z(-4 + -1z)) = 0
4((-4 * -7 + -1z * -7) + z(-4 + -1z)) = 0
4((28 + 7z) + z(-4 + -1z)) = 0
4(28 + 7z + (-4 * z + -1z * z)) = 0
4(28 + 7z + (-4z + -1z2)) = 0

Combine like terms: 7z + -4z = 3z
4(28 + 3z + -1z2) = 0
(28 * 4 + 3z * 4 + -1z2 * 4) = 0
(112 + 12z + -4z2) = 0

Solving
112 + 12z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(28 + 3z + -1z2) = 0

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

Ignore the factor 4.

Subproblem 1
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 2
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Solution
z = {7, -4}

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