3x+7=x^2-2x-7

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


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

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

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

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

Solving for variable 'x'.

Reorder the terms:
7 + 7 + 3x + 2x + -1x2 = -7 + -2x + x2 + 7 + 2x + -1x2

Combine like terms: 7 + 7 = 14
14 + 3x + 2x + -1x2 = -7 + -2x + x2 + 7 + 2x + -1x2

Combine like terms: 3x + 2x = 5x
14 + 5x + -1x2 = -7 + -2x + x2 + 7 + 2x + -1x2

Reorder the terms:
14 + 5x + -1x2 = -7 + 7 + -2x + 2x + x2 + -1x2

Combine like terms: -7 + 7 = 0
14 + 5x + -1x2 = 0 + -2x + 2x + x2 + -1x2
14 + 5x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
14 + 5x + -1x2 = 0 + x2 + -1x2
14 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
14 + 5x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {7, -2}

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