-16x^2+520-12x=0

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Solution for -16x^2+520-12x=0 equation: 


Simplifying
-16x2 + 520 + -12x = 0

Reorder the terms:
520 + -12x + -16x2 = 0

Solving
520 + -12x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(130 + -3x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(130 + -3x + -4x2)' equal to zero and attempt to solve:

Simplifying
130 + -3x + -4x2 = 0

Solving
130 + -3x + -4x2 = 0

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

Divide each side by '-4'.
-32.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '32.5' to each side of the equation.
-32.5 + 0.75x + 32.5 + x2 = 0 + 32.5

Reorder the terms:
-32.5 + 32.5 + 0.75x + x2 = 0 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + 0.75x + x2 = 0 + 32.5
0.75x + x2 = 0 + 32.5

Combine like terms: 0 + 32.5 = 32.5
0.75x + x2 = 32.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 32.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 32.5 + 0.140625

Combine like terms: 32.5 + 0.140625 = 32.640625
0.140625 + 0.75x + x2 = 32.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 32.640625

Calculate the square root of the right side: 5.713197441

Break this problem into two subproblems by setting 
(x + 0.375) equal to 5.713197441 and -5.713197441.


Subproblem 1
x + 0.375 = 5.713197441

Simplifying
x + 0.375 = 5.713197441

Reorder the terms:
0.375 + x = 5.713197441

Solving
0.375 + x = 5.713197441

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 5.713197441 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 5.713197441 + -0.375
x = 5.713197441 + -0.375

Combine like terms: 5.713197441 + -0.375 = 5.338197441
x = 5.338197441

Simplifying
x = 5.338197441


Subproblem 2
x + 0.375 = -5.713197441

Simplifying
x + 0.375 = -5.713197441

Reorder the terms:
0.375 + x = -5.713197441

Solving
0.375 + x = -5.713197441

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -5.713197441 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -5.713197441 + -0.375
x = -5.713197441 + -0.375

Combine like terms: -5.713197441 + -0.375 = -6.088197441
x = -6.088197441

Simplifying
x = -6.088197441


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.338197441, -6.088197441}
Solution
x = {5.338197441, -6.088197441}

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