(x-3)(x-5)+15=(x+2)(x+5)

Solution for (x-3)(x-5)+15=(x+2)(x+5) equation:

Simplifying
(x + -3)(x + -5) + 15 = (x + 2)(x + 5)

Reorder the terms:
(-3 + x)(x + -5) + 15 = (x + 2)(x + 5)

Reorder the terms:
(-3 + x)(-5 + x) + 15 = (x + 2)(x + 5)

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x)) + 15 = (x + 2)(x + 5)
((-5 * -3 + x * -3) + x(-5 + x)) + 15 = (x + 2)(x + 5)
((15 + -3x) + x(-5 + x)) + 15 = (x + 2)(x + 5)
(15 + -3x + (-5 * x + x * x)) + 15 = (x + 2)(x + 5)
(15 + -3x + (-5x + x2)) + 15 = (x + 2)(x + 5)

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2) + 15 = (x + 2)(x + 5)

Reorder the terms:
15 + 15 + -8x + x2 = (x + 2)(x + 5)

Combine like terms: 15 + 15 = 30
30 + -8x + x2 = (x + 2)(x + 5)

Reorder the terms:
30 + -8x + x2 = (2 + x)(x + 5)

Reorder the terms:
30 + -8x + x2 = (2 + x)(5 + x)

Multiply (2 + x) * (5 + x)
30 + -8x + x2 = (2(5 + x) + x(5 + x))
30 + -8x + x2 = ((5 * 2 + x * 2) + x(5 + x))
30 + -8x + x2 = ((10 + 2x) + x(5 + x))
30 + -8x + x2 = (10 + 2x + (5 * x + x * x))
30 + -8x + x2 = (10 + 2x + (5x + x2))

Combine like terms: 2x + 5x = 7x
30 + -8x + x2 = (10 + 7x + x2)

Add '-1x2' to each side of the equation.
30 + -8x + x2 + -1x2 = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -8x + 0 = 10 + 7x + x2 + -1x2
30 + -8x = 10 + 7x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -8x = 10 + 7x + 0
30 + -8x = 10 + 7x

Solving
30 + -8x = 10 + 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.
30 + -8x + -7x = 10 + 7x + -7x

Combine like terms: -8x + -7x = -15x
30 + -15x = 10 + 7x + -7x

Combine like terms: 7x + -7x = 0
30 + -15x = 10 + 0
30 + -15x = 10

Add '-30' to each side of the equation.
30 + -30 + -15x = 10 + -30

Combine like terms: 30 + -30 = 0
0 + -15x = 10 + -30
-15x = 10 + -30

Combine like terms: 10 + -30 = -20
-15x = -20

Divide each side by '-15'.
x = 1.333333333

Simplifying
x = 1.333333333