4(v-5)(-v-7)=0

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Solution for 4(v-5)(-v-7)=0 equation: 


Simplifying
4(v + -5)(-1v + -7) = 0

Reorder the terms:
4(-5 + v)(-1v + -7) = 0

Reorder the terms:
4(-5 + v)(-7 + -1v) = 0

Multiply (-5 + v) * (-7 + -1v)
4(-5(-7 + -1v) + v(-7 + -1v)) = 0
4((-7 * -5 + -1v * -5) + v(-7 + -1v)) = 0
4((35 + 5v) + v(-7 + -1v)) = 0
4(35 + 5v + (-7 * v + -1v * v)) = 0
4(35 + 5v + (-7v + -1v2)) = 0

Combine like terms: 5v + -7v = -2v
4(35 + -2v + -1v2) = 0
(35 * 4 + -2v * 4 + -1v2 * 4) = 0
(140 + -8v + -4v2) = 0

Solving
140 + -8v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -2v + -1v2) = 0

Factor a trinomial.
4((5 + -1v)(7 + v)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5

Subproblem 2
Set the factor '(7 + v)' equal to zero and attempt to solve:

Simplifying
7 + v = 0

Solving
7 + v = 0

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

Add '-7' to each side of the equation.
7 + -7 + v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + v = 0 + -7
v = 0 + -7

Combine like terms: 0 + -7 = -7
v = -7

Simplifying
v = -7
Solution
v = {5, -7}

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