(2v-5)(7v+1)=9v^2-60v-33

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Solution for (2v-5)(7v+1)=9v^2-60v-33 equation: 


Simplifying
(2v + -5)(7v + 1) = 9v2 + -60v + -33

Reorder the terms:
(-5 + 2v)(7v + 1) = 9v2 + -60v + -33

Reorder the terms:
(-5 + 2v)(1 + 7v) = 9v2 + -60v + -33

Multiply (-5 + 2v) * (1 + 7v)
(-5(1 + 7v) + 2v * (1 + 7v)) = 9v2 + -60v + -33
((1 * -5 + 7v * -5) + 2v * (1 + 7v)) = 9v2 + -60v + -33
((-5 + -35v) + 2v * (1 + 7v)) = 9v2 + -60v + -33
(-5 + -35v + (1 * 2v + 7v * 2v)) = 9v2 + -60v + -33
(-5 + -35v + (2v + 14v2)) = 9v2 + -60v + -33

Combine like terms: -35v + 2v = -33v
(-5 + -33v + 14v2) = 9v2 + -60v + -33

Reorder the terms:
-5 + -33v + 14v2 = -33 + -60v + 9v2

Solving
-5 + -33v + 14v2 = -33 + -60v + 9v2

Solving for variable 'v'.

Reorder the terms:
-5 + 33 + -33v + 60v + 14v2 + -9v2 = -33 + -60v + 9v2 + 33 + 60v + -9v2

Combine like terms: -5 + 33 = 28
28 + -33v + 60v + 14v2 + -9v2 = -33 + -60v + 9v2 + 33 + 60v + -9v2

Combine like terms: -33v + 60v = 27v
28 + 27v + 14v2 + -9v2 = -33 + -60v + 9v2 + 33 + 60v + -9v2

Combine like terms: 14v2 + -9v2 = 5v2
28 + 27v + 5v2 = -33 + -60v + 9v2 + 33 + 60v + -9v2

Reorder the terms:
28 + 27v + 5v2 = -33 + 33 + -60v + 60v + 9v2 + -9v2

Combine like terms: -33 + 33 = 0
28 + 27v + 5v2 = 0 + -60v + 60v + 9v2 + -9v2
28 + 27v + 5v2 = -60v + 60v + 9v2 + -9v2

Combine like terms: -60v + 60v = 0
28 + 27v + 5v2 = 0 + 9v2 + -9v2
28 + 27v + 5v2 = 9v2 + -9v2

Combine like terms: 9v2 + -9v2 = 0
28 + 27v + 5v2 = 0

Factor a trinomial.
(4 + v)(7 + 5v) = 0


Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v = 0 + -4
v = 0 + -4

Combine like terms: 0 + -4 = -4
v = -4

Simplifying
v = -4

Subproblem 2
Set the factor '(7 + 5v)' equal to zero and attempt to solve:

Simplifying
7 + 5v = 0

Solving
7 + 5v = 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 + 5v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5v = 0 + -7
5v = 0 + -7

Combine like terms: 0 + -7 = -7
5v = -7

Divide each side by '5'.
v = -1.4

Simplifying
v = -1.4
Solution
v = {-4, -1.4}

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