x^2=14x+32

Solution for x^2=14x+32 equation:

Simplifying
x2 = 14x + 32

Reorder the terms:
x2 = 32 + 14x

Solving
x2 = 32 + 14x

Solving for variable 'x'.

Reorder the terms:
-32 + -14x + x2 = 32 + 14x + -32 + -14x

Reorder the terms:
-32 + -14x + x2 = 32 + -32 + 14x + -14x

Combine like terms: 32 + -32 = 0
-32 + -14x + x2 = 0 + 14x + -14x
-32 + -14x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-32 + -14x + x2 = 0

Factor a trinomial.
(-2 + -1x)(16 + -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 '(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 = {-2, 16}