2x^2-6x+11=x^2+2x-4

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Solution for 2x^2-6x+11=x^2+2x-4 equation: 


Simplifying
2x2 + -6x + 11 = x2 + 2x + -4

Reorder the terms:
11 + -6x + 2x2 = x2 + 2x + -4

Reorder the terms:
11 + -6x + 2x2 = -4 + 2x + x2

Solving
11 + -6x + 2x2 = -4 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
11 + 4 + -6x + -2x + 2x2 + -1x2 = -4 + 2x + x2 + 4 + -2x + -1x2

Combine like terms: 11 + 4 = 15
15 + -6x + -2x + 2x2 + -1x2 = -4 + 2x + x2 + 4 + -2x + -1x2

Combine like terms: -6x + -2x = -8x
15 + -8x + 2x2 + -1x2 = -4 + 2x + x2 + 4 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
15 + -8x + 1x2 = -4 + 2x + x2 + 4 + -2x + -1x2

Reorder the terms:
15 + -8x + 1x2 = -4 + 4 + 2x + -2x + x2 + -1x2

Combine like terms: -4 + 4 = 0
15 + -8x + 1x2 = 0 + 2x + -2x + x2 + -1x2
15 + -8x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
15 + -8x + 1x2 = 0 + x2 + -1x2
15 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -8x + 1x2 = 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}

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