(x+4)(x+2)=(x-2)(x+9)

Solution for (x+4)(x+2)=(x-2)(x+9) equation:

Simplifying
(x + 4)(x + 2) = (x + -2)(x + 9)

Reorder the terms:
(4 + x)(x + 2) = (x + -2)(x + 9)

Reorder the terms:
(4 + x)(2 + x) = (x + -2)(x + 9)

Multiply (4 + x) * (2 + x)
(4(2 + x) + x(2 + x)) = (x + -2)(x + 9)
((2 * 4 + x * 4) + x(2 + x)) = (x + -2)(x + 9)
((8 + 4x) + x(2 + x)) = (x + -2)(x + 9)
(8 + 4x + (2 * x + x * x)) = (x + -2)(x + 9)
(8 + 4x + (2x + x2)) = (x + -2)(x + 9)

Combine like terms: 4x + 2x = 6x
(8 + 6x + x2) = (x + -2)(x + 9)

Reorder the terms:
8 + 6x + x2 = (-2 + x)(x + 9)

Reorder the terms:
8 + 6x + x2 = (-2 + x)(9 + x)

Multiply (-2 + x) * (9 + x)
8 + 6x + x2 = (-2(9 + x) + x(9 + x))
8 + 6x + x2 = ((9 * -2 + x * -2) + x(9 + x))
8 + 6x + x2 = ((-18 + -2x) + x(9 + x))
8 + 6x + x2 = (-18 + -2x + (9 * x + x * x))
8 + 6x + x2 = (-18 + -2x + (9x + x2))

Combine like terms: -2x + 9x = 7x
8 + 6x + x2 = (-18 + 7x + x2)

Add '-1x2' to each side of the equation.
8 + 6x + x2 + -1x2 = -18 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 6x + 0 = -18 + 7x + x2 + -1x2
8 + 6x = -18 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + 6x = -18 + 7x + 0
8 + 6x = -18 + 7x

Solving
8 + 6x = -18 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.
8 + 6x + -7x = -18 + 7x + -7x

Combine like terms: 6x + -7x = -1x
8 + -1x = -18 + 7x + -7x

Combine like terms: 7x + -7x = 0
8 + -1x = -18 + 0
8 + -1x = -18

Add '-8' to each side of the equation.
8 + -8 + -1x = -18 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = -18 + -8
-1x = -18 + -8

Combine like terms: -18 + -8 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26