x^2-11=10-4x

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Solution for x^2-11=10-4x equation: 


Simplifying
x2 + -11 = 10 + -4x

Reorder the terms:
-11 + x2 = 10 + -4x

Solving
-11 + x2 = 10 + -4x

Solving for variable 'x'.

Reorder the terms:
-11 + -10 + 4x + x2 = 10 + -4x + -10 + 4x

Combine like terms: -11 + -10 = -21
-21 + 4x + x2 = 10 + -4x + -10 + 4x

Reorder the terms:
-21 + 4x + x2 = 10 + -10 + -4x + 4x

Combine like terms: 10 + -10 = 0
-21 + 4x + x2 = 0 + -4x + 4x
-21 + 4x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

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 = {-7, 3}

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