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

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


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

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

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

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

Combine like terms: -4v + 7v = 3v
(-28 + 3v + v2) = 0

Solving
-28 + 3v + v2 = 0

Solving for variable 'v'.

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


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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