16(x-1)=x(x+8)

Solution for 16(x-1)=x(x+8) equation:

Simplifying
16(x + -1) = x(x + 8)

Reorder the terms:
16(-1 + x) = x(x + 8)
(-1 * 16 + x * 16) = x(x + 8)
(-16 + 16x) = x(x + 8)

Reorder the terms:
-16 + 16x = x(8 + x)
-16 + 16x = (8 * x + x * x)
-16 + 16x = (8x + x2)

Solving
-16 + 16x = 8x + x2

Solving for variable 'x'.

Combine like terms: 16x + -8x = 8x
-16 + 8x + -1x2 = 8x + x2 + -8x + -1x2

Reorder the terms:
-16 + 8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-16 + 8x + -1x2 = 0 + x2 + -1x2
-16 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 8x + -1x2 = 0

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

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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4
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 = {4, 4}