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

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

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

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

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

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

Combine like terms: -2x + 4x = 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.
(-5 + -1x)(3 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-5, 3}