(x+2)(x+5)=(x+3)(x-3)

Solution for (x+2)(x+5)=(x+3)(x-3) equation:

Simplifying
(x + 2)(x + 5) = (x + 3)(x + -3)

Reorder the terms:
(2 + x)(x + 5) = (x + 3)(x + -3)

Reorder the terms:
(2 + x)(5 + x) = (x + 3)(x + -3)

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) = (x + 3)(x + -3)
((5 * 2 + x * 2) + x(5 + x)) = (x + 3)(x + -3)
((10 + 2x) + x(5 + x)) = (x + 3)(x + -3)
(10 + 2x + (5 * x + x * x)) = (x + 3)(x + -3)
(10 + 2x + (5x + x2)) = (x + 3)(x + -3)

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) = (x + 3)(x + -3)

Reorder the terms:
10 + 7x + x2 = (3 + x)(x + -3)

Reorder the terms:
10 + 7x + x2 = (3 + x)(-3 + x)

Multiply (3 + x) * (-3 + x)
10 + 7x + x2 = (3(-3 + x) + x(-3 + x))
10 + 7x + x2 = ((-3 * 3 + x * 3) + x(-3 + x))
10 + 7x + x2 = ((-9 + 3x) + x(-3 + x))
10 + 7x + x2 = (-9 + 3x + (-3 * x + x * x))
10 + 7x + x2 = (-9 + 3x + (-3x + x2))

Combine like terms: 3x + -3x = 0
10 + 7x + x2 = (-9 + 0 + x2)
10 + 7x + x2 = (-9 + x2)

Add '-1x2' to each side of the equation.
10 + 7x + x2 + -1x2 = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 7x + 0 = -9 + x2 + -1x2
10 + 7x = -9 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + 7x = -9 + 0
10 + 7x = -9

Solving
10 + 7x = -9

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + 7x = -9 + -10

Combine like terms: 10 + -10 = 0
0 + 7x = -9 + -10
7x = -9 + -10

Combine like terms: -9 + -10 = -19
7x = -19

Divide each side by '7'.
x = -2.714285714

Simplifying
x = -2.714285714