4x=x^2-16x+64

Solution for 4x=x^2-16x+64 equation:

Simplifying
4x = x2 + -16x + 64

Reorder the terms:
4x = 64 + -16x + x2

Solving
4x = 64 + -16x + x2

Solving for variable 'x'.

Reorder the terms:
-64 + 4x + 16x + -1x2 = 64 + -16x + x2 + -64 + 16x + -1x2

Combine like terms: 4x + 16x = 20x
-64 + 20x + -1x2 = 64 + -16x + x2 + -64 + 16x + -1x2

Reorder the terms:
-64 + 20x + -1x2 = 64 + -64 + -16x + 16x + x2 + -1x2

Combine like terms: 64 + -64 = 0
-64 + 20x + -1x2 = 0 + -16x + 16x + x2 + -1x2
-64 + 20x + -1x2 = -16x + 16x + x2 + -1x2

Combine like terms: -16x + 16x = 0
-64 + 20x + -1x2 = 0 + x2 + -1x2
-64 + 20x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-64 + 20x + -1x2 = 0

Factor a trinomial.
(-16 + x)(4 + -1x) = 0

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

Simplifying
-16 + x = 0

Solving
-16 + x = 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 + x = 0 + 16

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

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

Simplifying
x = 16
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {16, 4}