(X-6)(X+3)=(X-2)(X+4)

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Solution for (X-6)(X+3)=(X-2)(X+4) equation: 


Simplifying
(X + -6)(X + 3) = (X + -2)(X + 4)

Reorder the terms:
(-6 + X)(X + 3) = (X + -2)(X + 4)

Reorder the terms:
(-6 + X)(3 + X) = (X + -2)(X + 4)

Multiply (-6 + X) * (3 + X)
(-6(3 + X) + X(3 + X)) = (X + -2)(X + 4)
((3 * -6 + X * -6) + X(3 + X)) = (X + -2)(X + 4)
((-18 + -6X) + X(3 + X)) = (X + -2)(X + 4)
(-18 + -6X + (3 * X + X * X)) = (X + -2)(X + 4)
(-18 + -6X + (3X + X2)) = (X + -2)(X + 4)

Combine like terms: -6X + 3X = -3X
(-18 + -3X + X2) = (X + -2)(X + 4)

Reorder the terms:
-18 + -3X + X2 = (-2 + X)(X + 4)

Reorder the terms:
-18 + -3X + X2 = (-2 + X)(4 + X)

Multiply (-2 + X) * (4 + X)
-18 + -3X + X2 = (-2(4 + X) + X(4 + X))
-18 + -3X + X2 = ((4 * -2 + X * -2) + X(4 + X))
-18 + -3X + X2 = ((-8 + -2X) + X(4 + X))
-18 + -3X + X2 = (-8 + -2X + (4 * X + X * X))
-18 + -3X + X2 = (-8 + -2X + (4X + X2))

Combine like terms: -2X + 4X = 2X
-18 + -3X + X2 = (-8 + 2X + X2)

Add '-1X2' to each side of the equation.
-18 + -3X + X2 + -1X2 = -8 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-18 + -3X + 0 = -8 + 2X + X2 + -1X2
-18 + -3X = -8 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-18 + -3X = -8 + 2X + 0
-18 + -3X = -8 + 2X

Solving
-18 + -3X = -8 + 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.
-18 + -3X + -2X = -8 + 2X + -2X

Combine like terms: -3X + -2X = -5X
-18 + -5X = -8 + 2X + -2X

Combine like terms: 2X + -2X = 0
-18 + -5X = -8 + 0
-18 + -5X = -8

Add '18' to each side of the equation.
-18 + 18 + -5X = -8 + 18

Combine like terms: -18 + 18 = 0
0 + -5X = -8 + 18
-5X = -8 + 18

Combine like terms: -8 + 18 = 10
-5X = 10

Divide each side by '-5'.
X = -2

Simplifying
X = -2

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