x^2+7x+5=x+12

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Solution for x^2+7x+5=x+12 equation: 


Simplifying
x2 + 7x + 5 = x + 12

Reorder the terms:
5 + 7x + x2 = x + 12

Reorder the terms:
5 + 7x + x2 = 12 + x

Solving
5 + 7x + x2 = 12 + x

Solving for variable 'x'.

Reorder the terms:
5 + -12 + 7x + -1x + x2 = 12 + x + -12 + -1x

Combine like terms: 5 + -12 = -7
-7 + 7x + -1x + x2 = 12 + x + -12 + -1x

Combine like terms: 7x + -1x = 6x
-7 + 6x + x2 = 12 + x + -12 + -1x

Reorder the terms:
-7 + 6x + x2 = 12 + -12 + x + -1x

Combine like terms: 12 + -12 = 0
-7 + 6x + x2 = 0 + x + -1x
-7 + 6x + x2 = x + -1x

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

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

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