(x-4)(x+2)=7

Solution for (x-4)(x+2)=7 equation:

Simplifying
(x + -4)(x + 2) = 7

Reorder the terms:
(-4 + x)(x + 2) = 7

Reorder the terms:
(-4 + x)(2 + x) = 7

Multiply (-4 + x) * (2 + x)
(-4(2 + x) + x(2 + x)) = 7
((2 * -4 + x * -4) + x(2 + x)) = 7
((-8 + -4x) + x(2 + x)) = 7
(-8 + -4x + (2 * x + x * x)) = 7
(-8 + -4x + (2x + x2)) = 7

Combine like terms: -4x + 2x = -2x
(-8 + -2x + x2) = 7

Solving
-8 + -2x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-8 + -7 + -2x + x2 = 7 + -7

Combine like terms: -8 + -7 = -15
-15 + -2x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}