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

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

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

Reorder the terms:
4(1 + v)(-1v + -6) = 0

Reorder the terms:
4(1 + v)(-6 + -1v) = 0

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

Combine like terms: -1v + -6v = -7v
4(-6 + -7v + -1v2) = 0
(-6 * 4 + -7v * 4 + -1v2 * 4) = 0
(-24 + -28v + -4v2) = 0

Solving
-24 + -28v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(6 + 7v + v2) = 0

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

Ignore the factor -4.
Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

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

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

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

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

Simplifying
v = -1
Solution
v = {-6, -1}