(10-x)(6+x)=64

Solution for (10-x)(6+x)=64 equation:

Simplifying
(10 + -1x)(6 + x) = 64

Multiply (10 + -1x) * (6 + x)
(10(6 + x) + -1x * (6 + x)) = 64
((6 * 10 + x * 10) + -1x * (6 + x)) = 64
((60 + 10x) + -1x * (6 + x)) = 64
(60 + 10x + (6 * -1x + x * -1x)) = 64
(60 + 10x + (-6x + -1x2)) = 64

Combine like terms: 10x + -6x = 4x
(60 + 4x + -1x2) = 64

Solving
60 + 4x + -1x2 = 64

Solving for variable 'x'.

Reorder the terms:
60 + -64 + 4x + -1x2 = 64 + -64

Combine like terms: 60 + -64 = -4
-4 + 4x + -1x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-4 + 4x + -1x2 = 0

Factor a trinomial.
(-2 + x)(2 + -1x) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 2}