-16x^2+156x-60=

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Solution for -16x^2+156x-60= equation: 


Simplifying
-16x2 + 156x + -60 = 0

Reorder the terms:
-60 + 156x + -16x2 = 0

Solving
-60 + 156x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 39x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + 39x + -4x2)' equal to zero and attempt to solve:

Simplifying
-15 + 39x + -4x2 = 0

Solving
-15 + 39x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
3.75 + -9.75x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -9.75x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -9.75x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -9.75x + x2 = 0 + -3.75
-9.75x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-9.75x + x2 = -3.75

The x term is -9.75x.  Take half its coefficient (-4.875).
Square it (23.765625) and add it to both sides.

Add '23.765625' to each side of the equation.
-9.75x + 23.765625 + x2 = -3.75 + 23.765625

Reorder the terms:
23.765625 + -9.75x + x2 = -3.75 + 23.765625

Combine like terms: -3.75 + 23.765625 = 20.015625
23.765625 + -9.75x + x2 = 20.015625

Factor a perfect square on the left side:
(x + -4.875)(x + -4.875) = 20.015625

Calculate the square root of the right side: 4.473882542

Break this problem into two subproblems by setting 
(x + -4.875) equal to 4.473882542 and -4.473882542.


Subproblem 1
x + -4.875 = 4.473882542

Simplifying
x + -4.875 = 4.473882542

Reorder the terms:
-4.875 + x = 4.473882542

Solving
-4.875 + x = 4.473882542

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = 4.473882542 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = 4.473882542 + 4.875
x = 4.473882542 + 4.875

Combine like terms: 4.473882542 + 4.875 = 9.348882542
x = 9.348882542

Simplifying
x = 9.348882542


Subproblem 2
x + -4.875 = -4.473882542

Simplifying
x + -4.875 = -4.473882542

Reorder the terms:
-4.875 + x = -4.473882542

Solving
-4.875 + x = -4.473882542

Solving for variable 'x'.

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

Add '4.875' to each side of the equation.
-4.875 + 4.875 + x = -4.473882542 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + x = -4.473882542 + 4.875
x = -4.473882542 + 4.875

Combine like terms: -4.473882542 + 4.875 = 0.401117458
x = 0.401117458

Simplifying
x = 0.401117458


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.348882542, 0.401117458}
Solution
x = {9.348882542, 0.401117458}

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