2v^2-16v+30=(v-3)(v-3)

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Solution for 2v^2-16v+30=(v-3)(v-3) equation: 


Simplifying
2v2 + -16v + 30 = (v + -3)(v + -3)

Reorder the terms:
30 + -16v + 2v2 = (v + -3)(v + -3)

Reorder the terms:
30 + -16v + 2v2 = (-3 + v)(v + -3)

Reorder the terms:
30 + -16v + 2v2 = (-3 + v)(-3 + v)

Multiply (-3 + v) * (-3 + v)
30 + -16v + 2v2 = (-3(-3 + v) + v(-3 + v))
30 + -16v + 2v2 = ((-3 * -3 + v * -3) + v(-3 + v))
30 + -16v + 2v2 = ((9 + -3v) + v(-3 + v))
30 + -16v + 2v2 = (9 + -3v + (-3 * v + v * v))
30 + -16v + 2v2 = (9 + -3v + (-3v + v2))

Combine like terms: -3v + -3v = -6v
30 + -16v + 2v2 = (9 + -6v + v2)

Solving
30 + -16v + 2v2 = 9 + -6v + v2

Solving for variable 'v'.

Reorder the terms:
30 + -9 + -16v + 6v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: 30 + -9 = 21
21 + -16v + 6v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: -16v + 6v = -10v
21 + -10v + 2v2 + -1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
21 + -10v + 1v2 = 9 + -6v + v2 + -9 + 6v + -1v2

Reorder the terms:
21 + -10v + 1v2 = 9 + -9 + -6v + 6v + v2 + -1v2

Combine like terms: 9 + -9 = 0
21 + -10v + 1v2 = 0 + -6v + 6v + v2 + -1v2
21 + -10v + 1v2 = -6v + 6v + v2 + -1v2

Combine like terms: -6v + 6v = 0
21 + -10v + 1v2 = 0 + v2 + -1v2
21 + -10v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
21 + -10v + 1v2 = 0

Factor a trinomial.
(3 + -1v)(7 + -1v) = 0


Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3

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 = {3, 7}

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