3x^2+x=x^2+10x+11

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Solution for 3x^2+x=x^2+10x+11 equation: 


Simplifying
3x2 + x = x2 + 10x + 11

Reorder the terms:
x + 3x2 = x2 + 10x + 11

Reorder the terms:
x + 3x2 = 11 + 10x + x2

Solving
x + 3x2 = 11 + 10x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + x + -10x + 3x2 + -1x2 = 11 + 10x + x2 + -11 + -10x + -1x2

Combine like terms: x + -10x = -9x
-11 + -9x + 3x2 + -1x2 = 11 + 10x + x2 + -11 + -10x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-11 + -9x + 2x2 = 11 + 10x + x2 + -11 + -10x + -1x2

Reorder the terms:
-11 + -9x + 2x2 = 11 + -11 + 10x + -10x + x2 + -1x2

Combine like terms: 11 + -11 = 0
-11 + -9x + 2x2 = 0 + 10x + -10x + x2 + -1x2
-11 + -9x + 2x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
-11 + -9x + 2x2 = 0 + x2 + -1x2
-11 + -9x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + -9x + 2x2 = 0

Factor a trinomial.
(-1 + -1x)(11 + -2x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

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

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-1, 5.5}

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