(x+3)(x+5)=(x+1)(x+9)

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Solution for (x+3)(x+5)=(x+1)(x+9) equation: 


Simplifying
(x + 3)(x + 5) = (x + 1)(x + 9)

Reorder the terms:
(3 + x)(x + 5) = (x + 1)(x + 9)

Reorder the terms:
(3 + x)(5 + x) = (x + 1)(x + 9)

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = (x + 1)(x + 9)
((5 * 3 + x * 3) + x(5 + x)) = (x + 1)(x + 9)
((15 + 3x) + x(5 + x)) = (x + 1)(x + 9)
(15 + 3x + (5 * x + x * x)) = (x + 1)(x + 9)
(15 + 3x + (5x + x2)) = (x + 1)(x + 9)

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = (x + 1)(x + 9)

Reorder the terms:
15 + 8x + x2 = (1 + x)(x + 9)

Reorder the terms:
15 + 8x + x2 = (1 + x)(9 + x)

Multiply (1 + x) * (9 + x)
15 + 8x + x2 = (1(9 + x) + x(9 + x))
15 + 8x + x2 = ((9 * 1 + x * 1) + x(9 + x))
15 + 8x + x2 = ((9 + 1x) + x(9 + x))
15 + 8x + x2 = (9 + 1x + (9 * x + x * x))
15 + 8x + x2 = (9 + 1x + (9x + x2))

Combine like terms: 1x + 9x = 10x
15 + 8x + x2 = (9 + 10x + x2)

Add '-1x2' to each side of the equation.
15 + 8x + x2 + -1x2 = 9 + 10x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 0 = 9 + 10x + x2 + -1x2
15 + 8x = 9 + 10x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x = 9 + 10x + 0
15 + 8x = 9 + 10x

Solving
15 + 8x = 9 + 10x

Solving for variable 'x'.

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

Add '-10x' to each side of the equation.
15 + 8x + -10x = 9 + 10x + -10x

Combine like terms: 8x + -10x = -2x
15 + -2x = 9 + 10x + -10x

Combine like terms: 10x + -10x = 0
15 + -2x = 9 + 0
15 + -2x = 9

Add '-15' to each side of the equation.
15 + -15 + -2x = 9 + -15

Combine like terms: 15 + -15 = 0
0 + -2x = 9 + -15
-2x = 9 + -15

Combine like terms: 9 + -15 = -6
-2x = -6

Divide each side by '-2'.
x = 3

Simplifying
x = 3

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