6v^2+25v+11=8(v+7)

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Solution for 6v^2+25v+11=8(v+7) equation: 


Simplifying
6v2 + 25v + 11 = 8(v + 7)

Reorder the terms:
11 + 25v + 6v2 = 8(v + 7)

Reorder the terms:
11 + 25v + 6v2 = 8(7 + v)
11 + 25v + 6v2 = (7 * 8 + v * 8)
11 + 25v + 6v2 = (56 + 8v)

Solving
11 + 25v + 6v2 = 56 + 8v

Solving for variable 'v'.

Reorder the terms:
11 + -56 + 25v + -8v + 6v2 = 56 + 8v + -56 + -8v

Combine like terms: 11 + -56 = -45
-45 + 25v + -8v + 6v2 = 56 + 8v + -56 + -8v

Combine like terms: 25v + -8v = 17v
-45 + 17v + 6v2 = 56 + 8v + -56 + -8v

Reorder the terms:
-45 + 17v + 6v2 = 56 + -56 + 8v + -8v

Combine like terms: 56 + -56 = 0
-45 + 17v + 6v2 = 0 + 8v + -8v
-45 + 17v + 6v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
-45 + 17v + 6v2 = 0

Factor a trinomial.
(-9 + -2v)(5 + -3v) = 0


Subproblem 1
Set the factor '(-9 + -2v)' equal to zero and attempt to solve:

Simplifying
-9 + -2v = 0

Solving
-9 + -2v = 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 + -2v = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2v = 0 + 9
-2v = 0 + 9

Combine like terms: 0 + 9 = 9
-2v = 9

Divide each side by '-2'.
v = -4.5

Simplifying
v = -4.5

Subproblem 2
Set the factor '(5 + -3v)' equal to zero and attempt to solve:

Simplifying
5 + -3v = 0

Solving
5 + -3v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3v = 0 + -5
-3v = 0 + -5

Combine like terms: 0 + -5 = -5
-3v = -5

Divide each side by '-3'.
v = 1.666666667

Simplifying
v = 1.666666667
Solution
v = {-4.5, 1.666666667}

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