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

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


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

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

Multiply (3 + x) * (-2 + x)
(3(-2 + x) + x(-2 + x)) = (x + -3)(x + 5)
((-2 * 3 + x * 3) + x(-2 + x)) = (x + -3)(x + 5)
((-6 + 3x) + x(-2 + x)) = (x + -3)(x + 5)
(-6 + 3x + (-2 * x + x * x)) = (x + -3)(x + 5)
(-6 + 3x + (-2x + x2)) = (x + -3)(x + 5)

Combine like terms: 3x + -2x = 1x
(-6 + 1x + x2) = (x + -3)(x + 5)

Reorder the terms:
-6 + 1x + x2 = (-3 + x)(x + 5)

Reorder the terms:
-6 + 1x + x2 = (-3 + x)(5 + x)

Multiply (-3 + x) * (5 + x)
-6 + 1x + x2 = (-3(5 + x) + x(5 + x))
-6 + 1x + x2 = ((5 * -3 + x * -3) + x(5 + x))
-6 + 1x + x2 = ((-15 + -3x) + x(5 + x))
-6 + 1x + x2 = (-15 + -3x + (5 * x + x * x))
-6 + 1x + x2 = (-15 + -3x + (5x + x2))

Combine like terms: -3x + 5x = 2x
-6 + 1x + x2 = (-15 + 2x + x2)

Add '-1x2' to each side of the equation.
-6 + 1x + x2 + -1x2 = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x + 0 = -15 + 2x + x2 + -1x2
-6 + 1x = -15 + 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + 1x = -15 + 2x + 0
-6 + 1x = -15 + 2x

Solving
-6 + 1x = -15 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-6 + 1x + -2x = -15 + 2x + -2x

Combine like terms: 1x + -2x = -1x
-6 + -1x = -15 + 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -1x = -15 + 0
-6 + -1x = -15

Add '6' to each side of the equation.
-6 + 6 + -1x = -15 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = -15 + 6
-1x = -15 + 6

Combine like terms: -15 + 6 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9

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