6v(v+9)=(2v+8)(v+9)

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Solution for 6v(v+9)=(2v+8)(v+9) equation: 


Simplifying
6v(v + 9) = (2v + 8)(v + 9)

Reorder the terms:
6v(9 + v) = (2v + 8)(v + 9)
(9 * 6v + v * 6v) = (2v + 8)(v + 9)
(54v + 6v2) = (2v + 8)(v + 9)

Reorder the terms:
54v + 6v2 = (8 + 2v)(v + 9)

Reorder the terms:
54v + 6v2 = (8 + 2v)(9 + v)

Multiply (8 + 2v) * (9 + v)
54v + 6v2 = (8(9 + v) + 2v * (9 + v))
54v + 6v2 = ((9 * 8 + v * 8) + 2v * (9 + v))
54v + 6v2 = ((72 + 8v) + 2v * (9 + v))
54v + 6v2 = (72 + 8v + (9 * 2v + v * 2v))
54v + 6v2 = (72 + 8v + (18v + 2v2))

Combine like terms: 8v + 18v = 26v
54v + 6v2 = (72 + 26v + 2v2)

Solving
54v + 6v2 = 72 + 26v + 2v2

Solving for variable 'v'.

Reorder the terms:
-72 + 54v + -26v + 6v2 + -2v2 = 72 + 26v + 2v2 + -72 + -26v + -2v2

Combine like terms: 54v + -26v = 28v
-72 + 28v + 6v2 + -2v2 = 72 + 26v + 2v2 + -72 + -26v + -2v2

Combine like terms: 6v2 + -2v2 = 4v2
-72 + 28v + 4v2 = 72 + 26v + 2v2 + -72 + -26v + -2v2

Reorder the terms:
-72 + 28v + 4v2 = 72 + -72 + 26v + -26v + 2v2 + -2v2

Combine like terms: 72 + -72 = 0
-72 + 28v + 4v2 = 0 + 26v + -26v + 2v2 + -2v2
-72 + 28v + 4v2 = 26v + -26v + 2v2 + -2v2

Combine like terms: 26v + -26v = 0
-72 + 28v + 4v2 = 0 + 2v2 + -2v2
-72 + 28v + 4v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-72 + 28v + 4v2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 7v + v2) = 0

Factor a trinomial.
4((-9 + -1v)(2 + -1v)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -1v)' equal to zero and attempt to solve:

Simplifying
-9 + -1v = 0

Solving
-9 + -1v = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1v = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1v = 0 + 9
-1v = 0 + 9

Combine like terms: 0 + 9 = 9
-1v = 9

Divide each side by '-1'.
v = -9

Simplifying
v = -9

Subproblem 2
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
Solution
v = {-9, 2}

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