(X-2)(X+5)=(X-1)(X+3)

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Solution for (X-2)(X+5)=(X-1)(X+3) equation: 


Simplifying
(X + -2)(X + 5) = (X + -1)(X + 3)

Reorder the terms:
(-2 + X)(X + 5) = (X + -1)(X + 3)

Reorder the terms:
(-2 + X)(5 + X) = (X + -1)(X + 3)

Multiply (-2 + X) * (5 + X)
(-2(5 + X) + X(5 + X)) = (X + -1)(X + 3)
((5 * -2 + X * -2) + X(5 + X)) = (X + -1)(X + 3)
((-10 + -2X) + X(5 + X)) = (X + -1)(X + 3)
(-10 + -2X + (5 * X + X * X)) = (X + -1)(X + 3)
(-10 + -2X + (5X + X2)) = (X + -1)(X + 3)

Combine like terms: -2X + 5X = 3X
(-10 + 3X + X2) = (X + -1)(X + 3)

Reorder the terms:
-10 + 3X + X2 = (-1 + X)(X + 3)

Reorder the terms:
-10 + 3X + X2 = (-1 + X)(3 + X)

Multiply (-1 + X) * (3 + X)
-10 + 3X + X2 = (-1(3 + X) + X(3 + X))
-10 + 3X + X2 = ((3 * -1 + X * -1) + X(3 + X))
-10 + 3X + X2 = ((-3 + -1X) + X(3 + X))
-10 + 3X + X2 = (-3 + -1X + (3 * X + X * X))
-10 + 3X + X2 = (-3 + -1X + (3X + X2))

Combine like terms: -1X + 3X = 2X
-10 + 3X + X2 = (-3 + 2X + X2)

Add '-1X2' to each side of the equation.
-10 + 3X + X2 + -1X2 = -3 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-10 + 3X + 0 = -3 + 2X + X2 + -1X2
-10 + 3X = -3 + 2X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-10 + 3X = -3 + 2X + 0
-10 + 3X = -3 + 2X

Solving
-10 + 3X = -3 + 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.
-10 + 3X + -2X = -3 + 2X + -2X

Combine like terms: 3X + -2X = 1X
-10 + 1X = -3 + 2X + -2X

Combine like terms: 2X + -2X = 0
-10 + 1X = -3 + 0
-10 + 1X = -3

Add '10' to each side of the equation.
-10 + 10 + 1X = -3 + 10

Combine like terms: -10 + 10 = 0
0 + 1X = -3 + 10
1X = -3 + 10

Combine like terms: -3 + 10 = 7
1X = 7

Divide each side by '1'.
X = 7

Simplifying
X = 7

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