(x+5)(x+3)=(x+7)(x-3)

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Solution for (x+5)(x+3)=(x+7)(x-3) equation: 


Simplifying
(x + 5)(x + 3) = (x + 7)(x + -3)

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

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

Multiply (5 + x) * (3 + x)
(5(3 + x) + x(3 + x)) = (x + 7)(x + -3)
((3 * 5 + x * 5) + x(3 + x)) = (x + 7)(x + -3)
((15 + 5x) + x(3 + x)) = (x + 7)(x + -3)
(15 + 5x + (3 * x + x * x)) = (x + 7)(x + -3)
(15 + 5x + (3x + x2)) = (x + 7)(x + -3)

Combine like terms: 5x + 3x = 8x
(15 + 8x + x2) = (x + 7)(x + -3)

Reorder the terms:
15 + 8x + x2 = (7 + x)(x + -3)

Reorder the terms:
15 + 8x + x2 = (7 + x)(-3 + x)

Multiply (7 + x) * (-3 + x)
15 + 8x + x2 = (7(-3 + x) + x(-3 + x))
15 + 8x + x2 = ((-3 * 7 + x * 7) + x(-3 + x))
15 + 8x + x2 = ((-21 + 7x) + x(-3 + x))
15 + 8x + x2 = (-21 + 7x + (-3 * x + x * x))
15 + 8x + x2 = (-21 + 7x + (-3x + x2))

Combine like terms: 7x + -3x = 4x
15 + 8x + x2 = (-21 + 4x + x2)

Add '-1x2' to each side of the equation.
15 + 8x + x2 + -1x2 = -21 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x + 0 = -21 + 4x + x2 + -1x2
15 + 8x = -21 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 8x = -21 + 4x + 0
15 + 8x = -21 + 4x

Solving
15 + 8x = -21 + 4x

Solving for variable 'x'.

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

Add '-4x' to each side of the equation.
15 + 8x + -4x = -21 + 4x + -4x

Combine like terms: 8x + -4x = 4x
15 + 4x = -21 + 4x + -4x

Combine like terms: 4x + -4x = 0
15 + 4x = -21 + 0
15 + 4x = -21

Add '-15' to each side of the equation.
15 + -15 + 4x = -21 + -15

Combine like terms: 15 + -15 = 0
0 + 4x = -21 + -15
4x = -21 + -15

Combine like terms: -21 + -15 = -36
4x = -36

Divide each side by '4'.
x = -9

Simplifying
x = -9

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