x^2=13x+48

Solution for x^2=13x+48 equation:

Simplifying
x2 = 13x + 48

Reorder the terms:
x2 = 48 + 13x

Solving
x2 = 48 + 13x

Solving for variable 'x'.

Reorder the terms:
-48 + -13x + x2 = 48 + 13x + -48 + -13x

Reorder the terms:
-48 + -13x + x2 = 48 + -48 + 13x + -13x

Combine like terms: 48 + -48 = 0
-48 + -13x + x2 = 0 + 13x + -13x
-48 + -13x + x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-48 + -13x + x2 = 0

Factor a trinomial.
(-3 + -1x)(16 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {-3, 16}