(x-4)(x+6)=56

Solution for (x-4)(x+6)=56 equation:

Simplifying
(x + -4)(x + 6) = 56

Reorder the terms:
(-4 + x)(x + 6) = 56

Reorder the terms:
(-4 + x)(6 + x) = 56

Multiply (-4 + x) * (6 + x)
(-4(6 + x) + x(6 + x)) = 56
((6 * -4 + x * -4) + x(6 + x)) = 56
((-24 + -4x) + x(6 + x)) = 56
(-24 + -4x + (6 * x + x * x)) = 56
(-24 + -4x + (6x + x2)) = 56

Combine like terms: -4x + 6x = 2x
(-24 + 2x + x2) = 56

Solving
-24 + 2x + x2 = 56

Solving for variable 'x'.

Reorder the terms:
-24 + -56 + 2x + x2 = 56 + -56

Combine like terms: -24 + -56 = -80
-80 + 2x + x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-80 + 2x + x2 = 0

Factor a trinomial.
(-10 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
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
Solution
x = {-10, 8}