-15x^2+120x-160=0

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Solution for -15x^2+120x-160=0 equation: 


Simplifying
-15x2 + 120x + -160 = 0

Reorder the terms:
-160 + 120x + -15x2 = 0

Solving
-160 + 120x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-32 + 24x + -3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-32 + 24x + -3x2)' equal to zero and attempt to solve:

Simplifying
-32 + 24x + -3x2 = 0

Solving
-32 + 24x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
10.66666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-10.66666667' to each side of the equation.
10.66666667 + -8x + -10.66666667 + x2 = 0 + -10.66666667

Reorder the terms:
10.66666667 + -10.66666667 + -8x + x2 = 0 + -10.66666667

Combine like terms: 10.66666667 + -10.66666667 = 0.00000000
0.00000000 + -8x + x2 = 0 + -10.66666667
-8x + x2 = 0 + -10.66666667

Combine like terms: 0 + -10.66666667 = -10.66666667
-8x + x2 = -10.66666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -10.66666667 + 16

Reorder the terms:
16 + -8x + x2 = -10.66666667 + 16

Combine like terms: -10.66666667 + 16 = 5.33333333
16 + -8x + x2 = 5.33333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 5.33333333

Calculate the square root of the right side: 2.309401076

Break this problem into two subproblems by setting 
(x + -4) equal to 2.309401076 and -2.309401076.


Subproblem 1
x + -4 = 2.309401076

Simplifying
x + -4 = 2.309401076

Reorder the terms:
-4 + x = 2.309401076

Solving
-4 + x = 2.309401076

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 2.309401076 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.309401076 + 4
x = 2.309401076 + 4

Combine like terms: 2.309401076 + 4 = 6.309401076
x = 6.309401076

Simplifying
x = 6.309401076


Subproblem 2
x + -4 = -2.309401076

Simplifying
x + -4 = -2.309401076

Reorder the terms:
-4 + x = -2.309401076

Solving
-4 + x = -2.309401076

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -2.309401076 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.309401076 + 4
x = -2.309401076 + 4

Combine like terms: -2.309401076 + 4 = 1.690598924
x = 1.690598924

Simplifying
x = 1.690598924


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.309401076, 1.690598924}
Solution
x = {6.309401076, 1.690598924}

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