(X+2)(X+3)=(X-4)(X-5)

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Solution for (X+2)(X+3)=(X-4)(X-5) equation: 


Simplifying
(X + 2)(X + 3) = (X + -4)(X + -5)

Reorder the terms:
(2 + X)(X + 3) = (X + -4)(X + -5)

Reorder the terms:
(2 + X)(3 + X) = (X + -4)(X + -5)

Multiply (2 + X) * (3 + X)
(2(3 + X) + X(3 + X)) = (X + -4)(X + -5)
((3 * 2 + X * 2) + X(3 + X)) = (X + -4)(X + -5)
((6 + 2X) + X(3 + X)) = (X + -4)(X + -5)
(6 + 2X + (3 * X + X * X)) = (X + -4)(X + -5)
(6 + 2X + (3X + X2)) = (X + -4)(X + -5)

Combine like terms: 2X + 3X = 5X
(6 + 5X + X2) = (X + -4)(X + -5)

Reorder the terms:
6 + 5X + X2 = (-4 + X)(X + -5)

Reorder the terms:
6 + 5X + X2 = (-4 + X)(-5 + X)

Multiply (-4 + X) * (-5 + X)
6 + 5X + X2 = (-4(-5 + X) + X(-5 + X))
6 + 5X + X2 = ((-5 * -4 + X * -4) + X(-5 + X))
6 + 5X + X2 = ((20 + -4X) + X(-5 + X))
6 + 5X + X2 = (20 + -4X + (-5 * X + X * X))
6 + 5X + X2 = (20 + -4X + (-5X + X2))

Combine like terms: -4X + -5X = -9X
6 + 5X + X2 = (20 + -9X + X2)

Add '-1X2' to each side of the equation.
6 + 5X + X2 + -1X2 = 20 + -9X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
6 + 5X + 0 = 20 + -9X + X2 + -1X2
6 + 5X = 20 + -9X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
6 + 5X = 20 + -9X + 0
6 + 5X = 20 + -9X

Solving
6 + 5X = 20 + -9X

Solving for variable 'X'.

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

Add '9X' to each side of the equation.
6 + 5X + 9X = 20 + -9X + 9X

Combine like terms: 5X + 9X = 14X
6 + 14X = 20 + -9X + 9X

Combine like terms: -9X + 9X = 0
6 + 14X = 20 + 0
6 + 14X = 20

Add '-6' to each side of the equation.
6 + -6 + 14X = 20 + -6

Combine like terms: 6 + -6 = 0
0 + 14X = 20 + -6
14X = 20 + -6

Combine like terms: 20 + -6 = 14
14X = 14

Divide each side by '14'.
X = 1

Simplifying
X = 1

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