x^2=48-13x

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

Simplifying
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.
(-16 + -1x)(3 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-16, 3}