6((-7+-1v)(4+-1v))=0

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Solution for 6((-7+-1v)(4+-1v))=0 equation: 


Simplifying
6((-7 + -1v)(4 + -1v)) = 0

Multiply (-7 + -1v) * (4 + -1v)
6((-7(4 + -1v) + -1v * (4 + -1v))) = 0
6(((4 * -7 + -1v * -7) + -1v * (4 + -1v))) = 0
6(((-28 + 7v) + -1v * (4 + -1v))) = 0
6((-28 + 7v + (4 * -1v + -1v * -1v))) = 0
6((-28 + 7v + (-4v + 1v2))) = 0

Combine like terms: 7v + -4v = 3v
6((-28 + 3v + 1v2)) = 0
(-28 * 6 + 3v * 6 + 1v2 * 6) = 0
(-168 + 18v + 6v2) = 0

Solving
-168 + 18v + 6v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + 3v + v2) = 0

Factor a trinomial.
6((-7 + -1v)(4 + -1v)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-7 + -1v)' equal to zero and attempt to solve:

Simplifying
-7 + -1v = 0

Solving
-7 + -1v = 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 + -1v = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1v = 0 + 7
-1v = 0 + 7

Combine like terms: 0 + 7 = 7
-1v = 7

Divide each side by '-1'.
v = -7

Simplifying
v = -7

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

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

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

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