49v^2+275v-76=8-5v

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Solution for 49v^2+275v-76=8-5v equation: 


Simplifying
49v2 + 275v + -76 = 8 + -5v

Reorder the terms:
-76 + 275v + 49v2 = 8 + -5v

Solving
-76 + 275v + 49v2 = 8 + -5v

Solving for variable 'v'.

Reorder the terms:
-76 + -8 + 275v + 5v + 49v2 = 8 + -5v + -8 + 5v

Combine like terms: -76 + -8 = -84
-84 + 275v + 5v + 49v2 = 8 + -5v + -8 + 5v

Combine like terms: 275v + 5v = 280v
-84 + 280v + 49v2 = 8 + -5v + -8 + 5v

Reorder the terms:
-84 + 280v + 49v2 = 8 + -8 + -5v + 5v

Combine like terms: 8 + -8 = 0
-84 + 280v + 49v2 = 0 + -5v + 5v
-84 + 280v + 49v2 = -5v + 5v

Combine like terms: -5v + 5v = 0
-84 + 280v + 49v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-12 + 40v + 7v2) = 0

Factor a trinomial.
7((-6 + -1v)(2 + -7v)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6

Subproblem 2
Set the factor '(2 + -7v)' equal to zero and attempt to solve:

Simplifying
2 + -7v = 0

Solving
2 + -7v = 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 + -7v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7v = 0 + -2
-7v = 0 + -2

Combine like terms: 0 + -2 = -2
-7v = -2

Divide each side by '-7'.
v = 0.2857142857

Simplifying
v = 0.2857142857
Solution
v = {-6, 0.2857142857}

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