12v(-20v)-(-10v)=(-18)

Solution for 12v(-20v)-(-10v)=(-18) equation:

Simplifying
12v(-20v) + -1(-10v) = (-18)

Remove parenthesis around (-20v)
12v * -20v + -1(-10v) = (-18)

Reorder the terms for easier multiplication:
12 * -20v * v + -1(-10v) = (-18)

Multiply 12 * -20
-240v * v + -1(-10v) = (-18)

Multiply v * v
-240v2 + -1(-10v) = (-18)

Remove parenthesis around (-10v)
-240v2 + -1 * -10v = (-18)

Multiply -1 * -10
-240v2 + 10v = (-18)

Reorder the terms:
10v + -240v2 = (-18)
10v + -240v2 = -18

Solving
10v + -240v2 = -18

Solving for variable 'v'.

Reorder the terms:
18 + 10v + -240v2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + 10v + -240v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 5v + -120v2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + 5v + -120v2)' equal to zero and attempt to solve:

Simplifying
9 + 5v + -120v2 = 0

Solving
9 + 5v + -120v2 = 0

Begin completing the square.  Divide all terms by
-120 the coefficient of the squared term: 

Divide each side by '-120'.
-0.075 + -0.04166666667v + v2 = 0.0

Move the constant term to the right:

Add '0.075' to each side of the equation.
-0.075 + -0.04166666667v + 0.075 + v2 = 0.0 + 0.075

Reorder the terms:
-0.075 + 0.075 + -0.04166666667v + v2 = 0.0 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + -0.04166666667v + v2 = 0.0 + 0.075
-0.04166666667v + v2 = 0.0 + 0.075

Combine like terms: 0.0 + 0.075 = 0.075
-0.04166666667v + v2 = 0.075

The v term is -0.04166666667v.  Take half its coefficient (-0.02083333334).
Square it (0.0004340277781) and add it to both sides.

Add '0.0004340277781' to each side of the equation.
-0.04166666667v + 0.0004340277781 + v2 = 0.075 + 0.0004340277781

Reorder the terms:
0.0004340277781 + -0.04166666667v + v2 = 0.075 + 0.0004340277781

Combine like terms: 0.075 + 0.0004340277781 = 0.0754340277781
0.0004340277781 + -0.04166666667v + v2 = 0.0754340277781

Factor a perfect square on the left side:
(v + -0.02083333334)(v + -0.02083333334) = 0.0754340277781

Calculate the square root of the right side: 0.274652558

Break this problem into two subproblems by setting 
(v + -0.02083333334) equal to 0.274652558 and -0.274652558.

Subproblem 1
v + -0.02083333334 = 0.274652558

Simplifying
v + -0.02083333334 = 0.274652558

Reorder the terms:
-0.02083333334 + v = 0.274652558

Solving
-0.02083333334 + v = 0.274652558

Solving for variable 'v'.

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

Add '0.02083333334' to each side of the equation.
-0.02083333334 + 0.02083333334 + v = 0.274652558 + 0.02083333334

Combine like terms: -0.02083333334 + 0.02083333334 = 0.00000000000
0.00000000000 + v = 0.274652558 + 0.02083333334
v = 0.274652558 + 0.02083333334

Combine like terms: 0.274652558 + 0.02083333334 = 0.29548589134
v = 0.29548589134

Simplifying
v = 0.29548589134

Subproblem 2
v + -0.02083333334 = -0.274652558

Simplifying
v + -0.02083333334 = -0.274652558

Reorder the terms:
-0.02083333334 + v = -0.274652558

Solving
-0.02083333334 + v = -0.274652558

Solving for variable 'v'.

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

Add '0.02083333334' to each side of the equation.
-0.02083333334 + 0.02083333334 + v = -0.274652558 + 0.02083333334

Combine like terms: -0.02083333334 + 0.02083333334 = 0.00000000000
0.00000000000 + v = -0.274652558 + 0.02083333334
v = -0.274652558 + 0.02083333334

Combine like terms: -0.274652558 + 0.02083333334 = -0.25381922466
v = -0.25381922466

Simplifying
v = -0.25381922466

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {0.29548589134, -0.25381922466}
Solution
v = {0.29548589134, -0.25381922466}