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

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


Simplifying
x2 + 7x = 2x2 + 5x + 1

Reorder the terms:
7x + x2 = 2x2 + 5x + 1

Reorder the terms:
7x + x2 = 1 + 5x + 2x2

Solving
7x + x2 = 1 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-1 + 7x + -5x + x2 + -2x2 = 1 + 5x + 2x2 + -1 + -5x + -2x2

Combine like terms: 7x + -5x = 2x
-1 + 2x + x2 + -2x2 = 1 + 5x + 2x2 + -1 + -5x + -2x2

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

Reorder the terms:
-1 + 2x + -1x2 = 1 + -1 + 5x + -5x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
-1 + 2x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2
-1 + 2x + -1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-1 + 2x + -1x2 = 0 + 2x2 + -2x2
-1 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-1 + 2x + -1x2 = 0

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


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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1

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 = {1, 1}

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