6(16+x)=x(10+x)

Solution for 6(16+x)=x(10+x) equation:

Simplifying
6(16 + x) = x(10 + x)
(16 * 6 + x * 6) = x(10 + x)
(96 + 6x) = x(10 + x)
96 + 6x = (10 * x + x * x)
96 + 6x = (10x + x2)

Solving
96 + 6x = 10x + x2

Solving for variable 'x'.

Combine like terms: 6x + -10x = -4x
96 + -4x + -1x2 = 10x + x2 + -10x + -1x2

Reorder the terms:
96 + -4x + -1x2 = 10x + -10x + x2 + -1x2

Combine like terms: 10x + -10x = 0
96 + -4x + -1x2 = 0 + x2 + -1x2
96 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
96 + -4x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(12 + x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {8, -12}