-16x^2+90x-60=0

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Solution for -16x^2+90x-60=0 equation: 


Simplifying
-16x2 + 90x + -60 = 0

Reorder the terms:
-60 + 90x + -16x2 = 0

Solving
-60 + 90x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 45x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-30 + 45x + -8x2)' equal to zero and attempt to solve:

Simplifying
-30 + 45x + -8x2 = 0

Solving
-30 + 45x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
3.75 + -5.625x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -5.625x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -5.625x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -5.625x + x2 = 0 + -3.75
-5.625x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-5.625x + x2 = -3.75

The x term is -5.625x.  Take half its coefficient (-2.8125).
Square it (7.91015625) and add it to both sides.

Add '7.91015625' to each side of the equation.
-5.625x + 7.91015625 + x2 = -3.75 + 7.91015625

Reorder the terms:
7.91015625 + -5.625x + x2 = -3.75 + 7.91015625

Combine like terms: -3.75 + 7.91015625 = 4.16015625
7.91015625 + -5.625x + x2 = 4.16015625

Factor a perfect square on the left side:
(x + -2.8125)(x + -2.8125) = 4.16015625

Calculate the square root of the right side: 2.039646109

Break this problem into two subproblems by setting 
(x + -2.8125) equal to 2.039646109 and -2.039646109.


Subproblem 1
x + -2.8125 = 2.039646109

Simplifying
x + -2.8125 = 2.039646109

Reorder the terms:
-2.8125 + x = 2.039646109

Solving
-2.8125 + x = 2.039646109

Solving for variable 'x'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + x = 2.039646109 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + x = 2.039646109 + 2.8125
x = 2.039646109 + 2.8125

Combine like terms: 2.039646109 + 2.8125 = 4.852146109
x = 4.852146109

Simplifying
x = 4.852146109


Subproblem 2
x + -2.8125 = -2.039646109

Simplifying
x + -2.8125 = -2.039646109

Reorder the terms:
-2.8125 + x = -2.039646109

Solving
-2.8125 + x = -2.039646109

Solving for variable 'x'.

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

Add '2.8125' to each side of the equation.
-2.8125 + 2.8125 + x = -2.039646109 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + x = -2.039646109 + 2.8125
x = -2.039646109 + 2.8125

Combine like terms: -2.039646109 + 2.8125 = 0.772853891
x = 0.772853891

Simplifying
x = 0.772853891


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.852146109, 0.772853891}
Solution
x = {4.852146109, 0.772853891}

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