(x-3)(x-2)=(x+5)(x-3)+21

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Solution for (x-3)(x-2)=(x+5)(x-3)+21 equation: 


Simplifying
(x + -3)(x + -2) = (x + 5)(x + -3) + 21

Reorder the terms:
(-3 + x)(x + -2) = (x + 5)(x + -3) + 21

Reorder the terms:
(-3 + x)(-2 + x) = (x + 5)(x + -3) + 21

Multiply (-3 + x) * (-2 + x)
(-3(-2 + x) + x(-2 + x)) = (x + 5)(x + -3) + 21
((-2 * -3 + x * -3) + x(-2 + x)) = (x + 5)(x + -3) + 21
((6 + -3x) + x(-2 + x)) = (x + 5)(x + -3) + 21
(6 + -3x + (-2 * x + x * x)) = (x + 5)(x + -3) + 21
(6 + -3x + (-2x + x2)) = (x + 5)(x + -3) + 21

Combine like terms: -3x + -2x = -5x
(6 + -5x + x2) = (x + 5)(x + -3) + 21

Reorder the terms:
6 + -5x + x2 = (5 + x)(x + -3) + 21

Reorder the terms:
6 + -5x + x2 = (5 + x)(-3 + x) + 21

Multiply (5 + x) * (-3 + x)
6 + -5x + x2 = (5(-3 + x) + x(-3 + x)) + 21
6 + -5x + x2 = ((-3 * 5 + x * 5) + x(-3 + x)) + 21
6 + -5x + x2 = ((-15 + 5x) + x(-3 + x)) + 21
6 + -5x + x2 = (-15 + 5x + (-3 * x + x * x)) + 21
6 + -5x + x2 = (-15 + 5x + (-3x + x2)) + 21

Combine like terms: 5x + -3x = 2x
6 + -5x + x2 = (-15 + 2x + x2) + 21

Reorder the terms:
6 + -5x + x2 = -15 + 21 + 2x + x2

Combine like terms: -15 + 21 = 6
6 + -5x + x2 = 6 + 2x + x2

Add '-6' to each side of the equation.
6 + -5x + -6 + x2 = 6 + 2x + -6 + x2

Reorder the terms:
6 + -6 + -5x + x2 = 6 + 2x + -6 + x2

Combine like terms: 6 + -6 = 0
0 + -5x + x2 = 6 + 2x + -6 + x2
-5x + x2 = 6 + 2x + -6 + x2

Reorder the terms:
-5x + x2 = 6 + -6 + 2x + x2

Combine like terms: 6 + -6 = 0
-5x + x2 = 0 + 2x + x2
-5x + x2 = 2x + x2

Add '-1x2' to each side of the equation.
-5x + x2 + -1x2 = 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5x + 0 = 2x + x2 + -1x2
-5x = 2x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5x = 2x + 0
-5x = 2x

Solving
-5x = 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.
-5x + -2x = 2x + -2x

Combine like terms: -5x + -2x = -7x
-7x = 2x + -2x

Combine like terms: 2x + -2x = 0
-7x = 0

Divide each side by '-7'.
x = 0

Simplifying
x = 0

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