5v(v-2)-6=-6(-2v+3)-3v

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Solution for 5v(v-2)-6=-6(-2v+3)-3v equation:


Simplifying
5v(v + -2) + -6 = -6(-2v + 3) + -3v

Reorder the terms:
5v(-2 + v) + -6 = -6(-2v + 3) + -3v
(-2 * 5v + v * 5v) + -6 = -6(-2v + 3) + -3v
(-10v + 5v2) + -6 = -6(-2v + 3) + -3v

Reorder the terms:
-6 + -10v + 5v2 = -6(-2v + 3) + -3v

Reorder the terms:
-6 + -10v + 5v2 = -6(3 + -2v) + -3v
-6 + -10v + 5v2 = (3 * -6 + -2v * -6) + -3v
-6 + -10v + 5v2 = (-18 + 12v) + -3v

Combine like terms: 12v + -3v = 9v
-6 + -10v + 5v2 = -18 + 9v

Solving
-6 + -10v + 5v2 = -18 + 9v

Solving for variable 'v'.

Reorder the terms:
-6 + 18 + -10v + -9v + 5v2 = -18 + 9v + 18 + -9v

Combine like terms: -6 + 18 = 12
12 + -10v + -9v + 5v2 = -18 + 9v + 18 + -9v

Combine like terms: -10v + -9v = -19v
12 + -19v + 5v2 = -18 + 9v + 18 + -9v

Reorder the terms:
12 + -19v + 5v2 = -18 + 18 + 9v + -9v

Combine like terms: -18 + 18 = 0
12 + -19v + 5v2 = 0 + 9v + -9v
12 + -19v + 5v2 = 9v + -9v

Combine like terms: 9v + -9v = 0
12 + -19v + 5v2 = 0

Factor a trinomial.
(4 + -5v)(3 + -1v) = 0


Subproblem 1
Set the factor '(4 + -5v)' equal to zero and attempt to solve:

Simplifying
4 + -5v = 0

Solving
4 + -5v = 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 + -5v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5v = 0 + -4
-5v = 0 + -4

Combine like terms: 0 + -4 = -4
-5v = -4

Divide each side by '-5'.
v = 0.8

Simplifying
v = 0.8

Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 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 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {0.8, 3}

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