x^2-6+11=7x-5

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Solution for x^2-6+11=7x-5 equation: 


Simplifying
x2 + -6 + 11 = 7x + -5

Reorder the terms:
-6 + 11 + x2 = 7x + -5

Combine like terms: -6 + 11 = 5
5 + x2 = 7x + -5

Reorder the terms:
5 + x2 = -5 + 7x

Solving
5 + x2 = -5 + 7x

Solving for variable 'x'.

Reorder the terms:
5 + 5 + -7x + x2 = -5 + 7x + 5 + -7x

Combine like terms: 5 + 5 = 10
10 + -7x + x2 = -5 + 7x + 5 + -7x

Reorder the terms:
10 + -7x + x2 = -5 + 5 + 7x + -7x

Combine like terms: -5 + 5 = 0
10 + -7x + x2 = 0 + 7x + -7x
10 + -7x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
10 + -7x + x2 = 0

Factor a trinomial.
(2 + -1x)(5 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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 = {2, 5}

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