x^2+3x+7=9x+2

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Solution for x^2+3x+7=9x+2 equation: 


Simplifying
x2 + 3x + 7 = 9x + 2

Reorder the terms:
7 + 3x + x2 = 9x + 2

Reorder the terms:
7 + 3x + x2 = 2 + 9x

Solving
7 + 3x + x2 = 2 + 9x

Solving for variable 'x'.

Reorder the terms:
7 + -2 + 3x + -9x + x2 = 2 + 9x + -2 + -9x

Combine like terms: 7 + -2 = 5
5 + 3x + -9x + x2 = 2 + 9x + -2 + -9x

Combine like terms: 3x + -9x = -6x
5 + -6x + x2 = 2 + 9x + -2 + -9x

Reorder the terms:
5 + -6x + x2 = 2 + -2 + 9x + -9x

Combine like terms: 2 + -2 = 0
5 + -6x + x2 = 0 + 9x + -9x
5 + -6x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
5 + -6x + x2 = 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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