(X-5)(5x-1)+(x-5)(5x+10)=0

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Solution for (X-5)(5x-1)+(x-5)(5x+10)=0 equation: 


Simplifying
(X + -5)(5x + -1) + (x + -5)(5x + 10) = 0

Reorder the terms:
(-5 + X)(5x + -1) + (x + -5)(5x + 10) = 0

Reorder the terms:
(-5 + X)(-1 + 5x) + (x + -5)(5x + 10) = 0

Multiply (-5 + X) * (-1 + 5x)
(-5(-1 + 5x) + X(-1 + 5x)) + (x + -5)(5x + 10) = 0
((-1 * -5 + 5x * -5) + X(-1 + 5x)) + (x + -5)(5x + 10) = 0
((5 + -25x) + X(-1 + 5x)) + (x + -5)(5x + 10) = 0
(5 + -25x + (-1 * X + 5x * X)) + (x + -5)(5x + 10) = 0
(5 + -25x + (-1X + 5xX)) + (x + -5)(5x + 10) = 0

Reorder the terms:
(5 + -1X + -25x + 5xX) + (x + -5)(5x + 10) = 0
(5 + -1X + -25x + 5xX) + (x + -5)(5x + 10) = 0

Reorder the terms:
5 + -1X + -25x + 5xX + (-5 + x)(5x + 10) = 0

Reorder the terms:
5 + -1X + -25x + 5xX + (-5 + x)(10 + 5x) = 0

Multiply (-5 + x) * (10 + 5x)
5 + -1X + -25x + 5xX + (-5(10 + 5x) + x(10 + 5x)) = 0
5 + -1X + -25x + 5xX + ((10 * -5 + 5x * -5) + x(10 + 5x)) = 0
5 + -1X + -25x + 5xX + ((-50 + -25x) + x(10 + 5x)) = 0
5 + -1X + -25x + 5xX + (-50 + -25x + (10 * x + 5x * x)) = 0
5 + -1X + -25x + 5xX + (-50 + -25x + (10x + 5x2)) = 0

Combine like terms: -25x + 10x = -15x
5 + -1X + -25x + 5xX + (-50 + -15x + 5x2) = 0

Reorder the terms:
5 + -50 + -1X + -25x + -15x + 5xX + 5x2 = 0

Combine like terms: 5 + -50 = -45
-45 + -1X + -25x + -15x + 5xX + 5x2 = 0

Combine like terms: -25x + -15x = -40x
-45 + -1X + -40x + 5xX + 5x2 = 0

Solving
-45 + -1X + -40x + 5xX + 5x2 = 0

Solving for variable 'X'.

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

Add '45' to each side of the equation.
-45 + -1X + -40x + 5xX + 45 + 5x2 = 0 + 45

Reorder the terms:
-45 + 45 + -1X + -40x + 5xX + 5x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -1X + -40x + 5xX + 5x2 = 0 + 45
-1X + -40x + 5xX + 5x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-1X + -40x + 5xX + 5x2 = 45

Add '40x' to each side of the equation.
-1X + -40x + 5xX + 40x + 5x2 = 45 + 40x

Reorder the terms:
-1X + -40x + 40x + 5xX + 5x2 = 45 + 40x

Combine like terms: -40x + 40x = 0
-1X + 0 + 5xX + 5x2 = 45 + 40x
-1X + 5xX + 5x2 = 45 + 40x

Add '-5x2' to each side of the equation.
-1X + 5xX + 5x2 + -5x2 = 45 + 40x + -5x2

Combine like terms: 5x2 + -5x2 = 0
-1X + 5xX + 0 = 45 + 40x + -5x2
-1X + 5xX = 45 + 40x + -5x2

Reorder the terms:
-45 + -1X + -40x + 5xX + 5x2 = 45 + 40x + -5x2 + -45 + -40x + 5x2

Reorder the terms:
-45 + -1X + -40x + 5xX + 5x2 = 45 + -45 + 40x + -40x + -5x2 + 5x2

Combine like terms: 45 + -45 = 0
-45 + -1X + -40x + 5xX + 5x2 = 0 + 40x + -40x + -5x2 + 5x2
-45 + -1X + -40x + 5xX + 5x2 = 40x + -40x + -5x2 + 5x2

Combine like terms: 40x + -40x = 0
-45 + -1X + -40x + 5xX + 5x2 = 0 + -5x2 + 5x2
-45 + -1X + -40x + 5xX + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-45 + -1X + -40x + 5xX + 5x2 = 0

The solution to this equation could not be determined.

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