(v-2)(v-7)=0

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Solution for (v-2)(v-7)=0 equation: 


Simplifying
(v + -2)(v + -7) = 0

Reorder the terms:
(-2 + v)(v + -7) = 0

Reorder the terms:
(-2 + v)(-7 + v) = 0

Multiply (-2 + v) * (-7 + v)
(-2(-7 + v) + v(-7 + v)) = 0
((-7 * -2 + v * -2) + v(-7 + v)) = 0
((14 + -2v) + v(-7 + v)) = 0
(14 + -2v + (-7 * v + v * v)) = 0
(14 + -2v + (-7v + v2)) = 0

Combine like terms: -2v + -7v = -9v
(14 + -9v + v2) = 0

Solving
14 + -9v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(2 + -1v)(7 + -1v) = 0


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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

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 = {2, 7}

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