x^2-5=7x+13

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Solution for x^2-5=7x+13 equation: 


Simplifying
x2 + -5 = 7x + 13

Reorder the terms:
-5 + x2 = 7x + 13

Reorder the terms:
-5 + x2 = 13 + 7x

Solving
-5 + x2 = 13 + 7x

Solving for variable 'x'.

Reorder the terms:
-5 + -13 + -7x + x2 = 13 + 7x + -13 + -7x

Combine like terms: -5 + -13 = -18
-18 + -7x + x2 = 13 + 7x + -13 + -7x

Reorder the terms:
-18 + -7x + x2 = 13 + -13 + 7x + -7x

Combine like terms: 13 + -13 = 0
-18 + -7x + x2 = 0 + 7x + -7x
-18 + -7x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-18 + -7x + x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2, 9}

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