2x^2+2x+9=x^2+8x+16

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Solution for 2x^2+2x+9=x^2+8x+16 equation: 


Simplifying
2x2 + 2x + 9 = x2 + 8x + 16

Reorder the terms:
9 + 2x + 2x2 = x2 + 8x + 16

Reorder the terms:
9 + 2x + 2x2 = 16 + 8x + x2

Solving
9 + 2x + 2x2 = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
9 + -16 + 2x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 9 + -16 = -7
-7 + 2x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 2x + -8x = -6x
-7 + -6x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-7 + -6x + 1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
-7 + -6x + 1x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-7 + -6x + 1x2 = 0 + 8x + -8x + x2 + -1x2
-7 + -6x + 1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-7 + -6x + 1x2 = 0 + x2 + -1x2
-7 + -6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -6x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -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 '(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
Solution
x = {-1, 7}

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