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

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


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

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

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

Multiply (-4 + X) * (3 + x)
(-4(3 + x) + X(3 + x)) = (x + 5)(x + -2)
((3 * -4 + x * -4) + X(3 + x)) = (x + 5)(x + -2)
((-12 + -4x) + X(3 + x)) = (x + 5)(x + -2)
(-12 + -4x + (3 * X + x * X)) = (x + 5)(x + -2)
(-12 + -4x + (3X + xX)) = (x + 5)(x + -2)

Reorder the terms:
(-12 + 3X + -4x + xX) = (x + 5)(x + -2)
(-12 + 3X + -4x + xX) = (x + 5)(x + -2)

Reorder the terms:
-12 + 3X + -4x + xX = (5 + x)(x + -2)

Reorder the terms:
-12 + 3X + -4x + xX = (5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
-12 + 3X + -4x + xX = (5(-2 + x) + x(-2 + x))
-12 + 3X + -4x + xX = ((-2 * 5 + x * 5) + x(-2 + x))
-12 + 3X + -4x + xX = ((-10 + 5x) + x(-2 + x))
-12 + 3X + -4x + xX = (-10 + 5x + (-2 * x + x * x))
-12 + 3X + -4x + xX = (-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
-12 + 3X + -4x + xX = (-10 + 3x + x2)

Solving
-12 + 3X + -4x + xX = -10 + 3x + x2

Solving for variable 'X'.

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

Add '12' to each side of the equation.
-12 + 3X + -4x + 12 + xX = -10 + 3x + 12 + x2

Reorder the terms:
-12 + 12 + 3X + -4x + xX = -10 + 3x + 12 + x2

Combine like terms: -12 + 12 = 0
0 + 3X + -4x + xX = -10 + 3x + 12 + x2
3X + -4x + xX = -10 + 3x + 12 + x2

Reorder the terms:
3X + -4x + xX = -10 + 12 + 3x + x2

Combine like terms: -10 + 12 = 2
3X + -4x + xX = 2 + 3x + x2

Add '4x' to each side of the equation.
3X + -4x + 4x + xX = 2 + 3x + 4x + x2

Combine like terms: -4x + 4x = 0
3X + 0 + xX = 2 + 3x + 4x + x2
3X + xX = 2 + 3x + 4x + x2

Combine like terms: 3x + 4x = 7x
3X + xX = 2 + 7x + x2

Reorder the terms:
-2 + 3X + -7x + xX + -1x2 = 2 + 7x + x2 + -2 + -7x + -1x2

Reorder the terms:
-2 + 3X + -7x + xX + -1x2 = 2 + -2 + 7x + -7x + x2 + -1x2

Combine like terms: 2 + -2 = 0
-2 + 3X + -7x + xX + -1x2 = 0 + 7x + -7x + x2 + -1x2
-2 + 3X + -7x + xX + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
-2 + 3X + -7x + xX + -1x2 = 0 + x2 + -1x2
-2 + 3X + -7x + xX + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 3X + -7x + xX + -1x2 = 0

The solution to this equation could not be determined.

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