(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 = -55
-55 + 1X + -25x + -15x + 5xX + 5x2 = 0

Combine like terms: -25x + -15x = -40x
-55 + 1X + -40x + 5xX + 5x2 = 0

Solving
-55 + 1X + -40x + 5xX + 5x2 = 0

Solving for variable 'X'.

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

Add '55' to each side of the equation.
-55 + 1X + -40x + 5xX + 55 + 5x2 = 0 + 55

Reorder the terms:
-55 + 55 + 1X + -40x + 5xX + 5x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 1X + -40x + 5xX + 5x2 = 0 + 55
1X + -40x + 5xX + 5x2 = 0 + 55

Combine like terms: 0 + 55 = 55
1X + -40x + 5xX + 5x2 = 55

Add '40x' to each side of the equation.
1X + -40x + 5xX + 40x + 5x2 = 55 + 40x

Reorder the terms:
1X + -40x + 40x + 5xX + 5x2 = 55 + 40x

Combine like terms: -40x + 40x = 0
1X + 0 + 5xX + 5x2 = 55 + 40x
1X + 5xX + 5x2 = 55 + 40x

Add '-5x2' to each side of the equation.
1X + 5xX + 5x2 + -5x2 = 55 + 40x + -5x2

Combine like terms: 5x2 + -5x2 = 0
1X + 5xX + 0 = 55 + 40x + -5x2
1X + 5xX = 55 + 40x + -5x2

Reorder the terms:
-55 + 1X + -40x + 5xX + 5x2 = 55 + 40x + -5x2 + -55 + -40x + 5x2

Reorder the terms:
-55 + 1X + -40x + 5xX + 5x2 = 55 + -55 + 40x + -40x + -5x2 + 5x2

Combine like terms: 55 + -55 = 0
-55 + 1X + -40x + 5xX + 5x2 = 0 + 40x + -40x + -5x2 + 5x2
-55 + 1X + -40x + 5xX + 5x2 = 40x + -40x + -5x2 + 5x2

Combine like terms: 40x + -40x = 0
-55 + 1X + -40x + 5xX + 5x2 = 0 + -5x2 + 5x2
-55 + 1X + -40x + 5xX + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-55 + 1X + -40x + 5xX + 5x2 = 0

The solution to this equation could not be determined.

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