2.4v(v-1.4)=3.6(-v+2.8)

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Solution for 2.4v(v-1.4)=3.6(-v+2.8) equation: 


Simplifying
2.4v(v + -1.4) = 3.6(-1v + 2.8)

Reorder the terms:
2.4v(-1.4 + v) = 3.6(-1v + 2.8)
(-1.4 * 2.4v + v * 2.4v) = 3.6(-1v + 2.8)
(-3.36v + 2.4v2) = 3.6(-1v + 2.8)

Reorder the terms:
-3.36v + 2.4v2 = 3.6(2.8 + -1v)
-3.36v + 2.4v2 = (2.8 * 3.6 + -1v * 3.6)
-3.36v + 2.4v2 = (10.08 + -3.6v)

Solving
-3.36v + 2.4v2 = 10.08 + -3.6v

Solving for variable 'v'.

Reorder the terms:
-10.08 + -3.36v + 3.6v + 2.4v2 = 10.08 + -3.6v + -10.08 + 3.6v

Combine like terms: -3.36v + 3.6v = 0.24v
-10.08 + 0.24v + 2.4v2 = 10.08 + -3.6v + -10.08 + 3.6v

Reorder the terms:
-10.08 + 0.24v + 2.4v2 = 10.08 + -10.08 + -3.6v + 3.6v

Combine like terms: 10.08 + -10.08 = 0.00
-10.08 + 0.24v + 2.4v2 = 0.00 + -3.6v + 3.6v
-10.08 + 0.24v + 2.4v2 = -3.6v + 3.6v

Combine like terms: -3.6v + 3.6v = 0.0
-10.08 + 0.24v + 2.4v2 = 0.0

Begin completing the square.  Divide all terms by
2.4 the coefficient of the squared term: 

Divide each side by '2.4'.
-4.2 + 0.1v + v2 = 0

Move the constant term to the right:

Add '4.2' to each side of the equation.
-4.2 + 0.1v + 4.2 + v2 = 0 + 4.2

Reorder the terms:
-4.2 + 4.2 + 0.1v + v2 = 0 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + 0.1v + v2 = 0 + 4.2
0.1v + v2 = 0 + 4.2

Combine like terms: 0 + 4.2 = 4.2
0.1v + v2 = 4.2

The v term is 0.1v.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1v + 0.0025 + v2 = 4.2 + 0.0025

Reorder the terms:
0.0025 + 0.1v + v2 = 4.2 + 0.0025

Combine like terms: 4.2 + 0.0025 = 4.2025
0.0025 + 0.1v + v2 = 4.2025

Factor a perfect square on the left side:
(v + 0.05)(v + 0.05) = 4.2025

Calculate the square root of the right side: 2.05

Break this problem into two subproblems by setting 
(v + 0.05) equal to 2.05 and -2.05.


Subproblem 1
v + 0.05 = 2.05

Simplifying
v + 0.05 = 2.05

Reorder the terms:
0.05 + v = 2.05

Solving
0.05 + v = 2.05

Solving for variable 'v'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + v = 2.05 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + v = 2.05 + -0.05
v = 2.05 + -0.05

Combine like terms: 2.05 + -0.05 = 2
v = 2

Simplifying
v = 2


Subproblem 2
v + 0.05 = -2.05

Simplifying
v + 0.05 = -2.05

Reorder the terms:
0.05 + v = -2.05

Solving
0.05 + v = -2.05

Solving for variable 'v'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + v = -2.05 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + v = -2.05 + -0.05
v = -2.05 + -0.05

Combine like terms: -2.05 + -0.05 = -2.1
v = -2.1

Simplifying
v = -2.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2, -2.1}

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