x^2+4x+1=5x+7

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Solution for x^2+4x+1=5x+7 equation: 


Simplifying
x2 + 4x + 1 = 5x + 7

Reorder the terms:
1 + 4x + x2 = 5x + 7

Reorder the terms:
1 + 4x + x2 = 7 + 5x

Solving
1 + 4x + x2 = 7 + 5x

Solving for variable 'x'.

Reorder the terms:
1 + -7 + 4x + -5x + x2 = 7 + 5x + -7 + -5x

Combine like terms: 1 + -7 = -6
-6 + 4x + -5x + x2 = 7 + 5x + -7 + -5x

Combine like terms: 4x + -5x = -1x
-6 + -1x + x2 = 7 + 5x + -7 + -5x

Reorder the terms:
-6 + -1x + x2 = 7 + -7 + 5x + -5x

Combine like terms: 7 + -7 = 0
-6 + -1x + x2 = 0 + 5x + -5x
-6 + -1x + x2 = 5x + -5x

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

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 3}

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