1210v^2-447v-219=-9-7v

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Solution for 1210v^2-447v-219=-9-7v equation: 


Simplifying
1210v2 + -447v + -219 = -9 + -7v

Reorder the terms:
-219 + -447v + 1210v2 = -9 + -7v

Solving
-219 + -447v + 1210v2 = -9 + -7v

Solving for variable 'v'.

Reorder the terms:
-219 + 9 + -447v + 7v + 1210v2 = -9 + -7v + 9 + 7v

Combine like terms: -219 + 9 = -210
-210 + -447v + 7v + 1210v2 = -9 + -7v + 9 + 7v

Combine like terms: -447v + 7v = -440v
-210 + -440v + 1210v2 = -9 + -7v + 9 + 7v

Reorder the terms:
-210 + -440v + 1210v2 = -9 + 9 + -7v + 7v

Combine like terms: -9 + 9 = 0
-210 + -440v + 1210v2 = 0 + -7v + 7v
-210 + -440v + 1210v2 = -7v + 7v

Combine like terms: -7v + 7v = 0
-210 + -440v + 1210v2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-21 + -44v + 121v2) = 0

Factor a trinomial.
10((-3 + -11v)(7 + -11v)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-3 + -11v)' equal to zero and attempt to solve:

Simplifying
-3 + -11v = 0

Solving
-3 + -11v = 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 + -11v = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -11v = 0 + 3
-11v = 0 + 3

Combine like terms: 0 + 3 = 3
-11v = 3

Divide each side by '-11'.
v = -0.2727272727

Simplifying
v = -0.2727272727

Subproblem 2
Set the factor '(7 + -11v)' equal to zero and attempt to solve:

Simplifying
7 + -11v = 0

Solving
7 + -11v = 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 + -11v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -11v = 0 + -7
-11v = 0 + -7

Combine like terms: 0 + -7 = -7
-11v = -7

Divide each side by '-11'.
v = 0.6363636364

Simplifying
v = 0.6363636364
Solution
v = {-0.2727272727, 0.6363636364}

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