(x^2+4)=(8x-11)

Solution for (x^2+4)=(8x-11) equation:

Simplifying
(x2 + 4) = (8x + -11)

Reorder the terms:
(4 + x2) = (8x + -11)

Remove parenthesis around (4 + x2)
4 + x2 = (8x + -11)

Reorder the terms:
4 + x2 = (-11 + 8x)

Remove parenthesis around (-11 + 8x)
4 + x2 = -11 + 8x

Solving
4 + x2 = -11 + 8x

Solving for variable 'x'.

Reorder the terms:
4 + 11 + -8x + x2 = -11 + 8x + 11 + -8x

Combine like terms: 4 + 11 = 15
15 + -8x + x2 = -11 + 8x + 11 + -8x

Reorder the terms:
15 + -8x + x2 = -11 + 11 + 8x + -8x

Combine like terms: -11 + 11 = 0
15 + -8x + x2 = 0 + 8x + -8x
15 + -8x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
15 + -8x + x2 = 0

Factor a trinomial.
(3 + -1x)(5 + -1x) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {3, 5}