(x-7)=(x^2-49)

Solution for (x-7)=(x^2-49) equation:

Simplifying
(x + -7) = (x2 + -49)

Reorder the terms:
(-7 + x) = (x2 + -49)

Remove parenthesis around (-7 + x)
-7 + x = (x2 + -49)

Reorder the terms:
-7 + x = (-49 + x2)

Remove parenthesis around (-49 + x2)
-7 + x = -49 + x2

Solving
-7 + x = -49 + x2

Solving for variable 'x'.

Reorder the terms:
-7 + 49 + x + -1x2 = -49 + x2 + 49 + -1x2

Combine like terms: -7 + 49 = 42
42 + x + -1x2 = -49 + x2 + 49 + -1x2

Reorder the terms:
42 + x + -1x2 = -49 + 49 + x2 + -1x2

Combine like terms: -49 + 49 = 0
42 + x + -1x2 = 0 + x2 + -1x2
42 + x + -1x2 = x2 + -1x2

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

Factor a trinomial.
(7 + -1x)(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {7, -6}