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

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


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

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

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

Multiply (-5 + X) * (2 + X)
(-5(2 + X) + X(2 + X)) = (X + 4)(X + -3)
((2 * -5 + X * -5) + X(2 + X)) = (X + 4)(X + -3)
((-10 + -5X) + X(2 + X)) = (X + 4)(X + -3)
(-10 + -5X + (2 * X + X * X)) = (X + 4)(X + -3)
(-10 + -5X + (2X + X2)) = (X + 4)(X + -3)

Combine like terms: -5X + 2X = -3X
(-10 + -3X + X2) = (X + 4)(X + -3)

Reorder the terms:
-10 + -3X + X2 = (4 + X)(X + -3)

Reorder the terms:
-10 + -3X + X2 = (4 + X)(-3 + X)

Multiply (4 + X) * (-3 + X)
-10 + -3X + X2 = (4(-3 + X) + X(-3 + X))
-10 + -3X + X2 = ((-3 * 4 + X * 4) + X(-3 + X))
-10 + -3X + X2 = ((-12 + 4X) + X(-3 + X))
-10 + -3X + X2 = (-12 + 4X + (-3 * X + X * X))
-10 + -3X + X2 = (-12 + 4X + (-3X + X2))

Combine like terms: 4X + -3X = 1X
-10 + -3X + X2 = (-12 + 1X + X2)

Add '-1X2' to each side of the equation.
-10 + -3X + X2 + -1X2 = -12 + 1X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-10 + -3X + 0 = -12 + 1X + X2 + -1X2
-10 + -3X = -12 + 1X + X2 + -1X2

Combine like terms: X2 + -1X2 = 0
-10 + -3X = -12 + 1X + 0
-10 + -3X = -12 + 1X

Solving
-10 + -3X = -12 + 1X

Solving for variable 'X'.

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

Add '-1X' to each side of the equation.
-10 + -3X + -1X = -12 + 1X + -1X

Combine like terms: -3X + -1X = -4X
-10 + -4X = -12 + 1X + -1X

Combine like terms: 1X + -1X = 0
-10 + -4X = -12 + 0
-10 + -4X = -12

Add '10' to each side of the equation.
-10 + 10 + -4X = -12 + 10

Combine like terms: -10 + 10 = 0
0 + -4X = -12 + 10
-4X = -12 + 10

Combine like terms: -12 + 10 = -2
-4X = -2

Divide each side by '-4'.
X = 0.5

Simplifying
X = 0.5

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