2x^2+8x=x^2+33

Solution for 2x^2+8x=x^2+33 equation:

Simplifying
2x2 + 8x = x2 + 33

Reorder the terms:
8x + 2x2 = x2 + 33

Reorder the terms:
8x + 2x2 = 33 + x2

Solving
8x + 2x2 = 33 + x2

Solving for variable 'x'.

Reorder the terms:
-33 + 8x + 2x2 + -1x2 = 33 + x2 + -33 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-33 + 8x + 1x2 = 33 + x2 + -33 + -1x2

Reorder the terms:
-33 + 8x + 1x2 = 33 + -33 + x2 + -1x2

Combine like terms: 33 + -33 = 0
-33 + 8x + 1x2 = 0 + x2 + -1x2
-33 + 8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-33 + 8x + 1x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
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
Solution
x = {-11, 3}