3v(v-5)=7v+45

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Solution for 3v(v-5)=7v+45 equation: 


Simplifying
3v(v + -5) = 7v + 45

Reorder the terms:
3v(-5 + v) = 7v + 45
(-5 * 3v + v * 3v) = 7v + 45
(-15v + 3v2) = 7v + 45

Reorder the terms:
-15v + 3v2 = 45 + 7v

Solving
-15v + 3v2 = 45 + 7v

Solving for variable 'v'.

Reorder the terms:
-45 + -15v + -7v + 3v2 = 45 + 7v + -45 + -7v

Combine like terms: -15v + -7v = -22v
-45 + -22v + 3v2 = 45 + 7v + -45 + -7v

Reorder the terms:
-45 + -22v + 3v2 = 45 + -45 + 7v + -7v

Combine like terms: 45 + -45 = 0
-45 + -22v + 3v2 = 0 + 7v + -7v
-45 + -22v + 3v2 = 7v + -7v

Combine like terms: 7v + -7v = 0
-45 + -22v + 3v2 = 0

Factor a trinomial.
(-5 + -3v)(9 + -1v) = 0


Subproblem 1
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

Subproblem 2
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
Solution
v = {-1.666666667, 9}

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