(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 = -11v
(28 + -11v + v2) = 0

Solving
28 + -11v + v2 = 0

Solving for variable 'v'.

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


Subproblem 1
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

Subproblem 2
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
Solution
v = {4, 7}

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