(-x^2-3x+481)-(x^2+8x)=0

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Solution for (-x^2-3x+481)-(x^2+8x)=0 equation: 


Simplifying
(-1x2 + -3x + 481) + -1(x2 + 8x) = 0

Reorder the terms:
(481 + -3x + -1x2) + -1(x2 + 8x) = 0

Remove parenthesis around (481 + -3x + -1x2)
481 + -3x + -1x2 + -1(x2 + 8x) = 0

Reorder the terms:
481 + -3x + -1x2 + -1(8x + x2) = 0
481 + -3x + -1x2 + (8x * -1 + x2 * -1) = 0
481 + -3x + -1x2 + (-8x + -1x2) = 0

Reorder the terms:
481 + -3x + -8x + -1x2 + -1x2 = 0

Combine like terms: -3x + -8x = -11x
481 + -11x + -1x2 + -1x2 = 0

Combine like terms: -1x2 + -1x2 = -2x2
481 + -11x + -2x2 = 0

Solving
481 + -11x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(37 + 2x) = 0


Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

Subproblem 2
Set the factor '(37 + 2x)' equal to zero and attempt to solve:

Simplifying
37 + 2x = 0

Solving
37 + 2x = 0

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

Add '-37' to each side of the equation.
37 + -37 + 2x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 2x = 0 + -37
2x = 0 + -37

Combine like terms: 0 + -37 = -37
2x = -37

Divide each side by '2'.
x = -18.5

Simplifying
x = -18.5
Solution
x = {13, -18.5}

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