2x^2-2x+9=x^2+4x+4

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Solution for 2x^2-2x+9=x^2+4x+4 equation: 


Simplifying
2x2 + -2x + 9 = x2 + 4x + 4

Reorder the terms:
9 + -2x + 2x2 = x2 + 4x + 4

Reorder the terms:
9 + -2x + 2x2 = 4 + 4x + x2

Solving
9 + -2x + 2x2 = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -4 + -2x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 9 + -4 = 5
5 + -2x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: -2x + -4x = -6x
5 + -6x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
5 + -6x + 1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
5 + -6x + 1x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
5 + -6x + 1x2 = 0 + 4x + -4x + x2 + -1x2
5 + -6x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
5 + -6x + 1x2 = 0 + x2 + -1x2
5 + -6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + -6x + 1x2 = 0

Factor a trinomial.
(1 + -1x)(5 + -1x) = 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 '(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 = {1, 5}

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