(X^2-x-20)(5x-20)=0

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Solution for (X^2-x-20)(5x-20)=0 equation: 


Simplifying
(X2 + -1x + -20)(5x + -20) = 0

Reorder the terms:
(-20 + X2 + -1x)(5x + -20) = 0

Reorder the terms:
(-20 + X2 + -1x)(-20 + 5x) = 0

Multiply (-20 + X2 + -1x) * (-20 + 5x)
(-20(-20 + 5x) + X2(-20 + 5x) + -1x * (-20 + 5x)) = 0
((-20 * -20 + 5x * -20) + X2(-20 + 5x) + -1x * (-20 + 5x)) = 0
((400 + -100x) + X2(-20 + 5x) + -1x * (-20 + 5x)) = 0
(400 + -100x + (-20 * X2 + 5x * X2) + -1x * (-20 + 5x)) = 0
(400 + -100x + (-20X2 + 5xX2) + -1x * (-20 + 5x)) = 0
(400 + -100x + -20X2 + 5xX2 + (-20 * -1x + 5x * -1x)) = 0
(400 + -100x + -20X2 + 5xX2 + (20x + -5x2)) = 0

Reorder the terms:
(400 + -20X2 + -100x + 20x + 5xX2 + -5x2) = 0

Combine like terms: -100x + 20x = -80x
(400 + -20X2 + -80x + 5xX2 + -5x2) = 0

Solving
400 + -20X2 + -80x + 5xX2 + -5x2 = 0

Solving for variable 'X'.

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

Add '-400' to each side of the equation.
400 + -20X2 + -80x + 5xX2 + -400 + -5x2 = 0 + -400

Reorder the terms:
400 + -400 + -20X2 + -80x + 5xX2 + -5x2 = 0 + -400

Combine like terms: 400 + -400 = 0
0 + -20X2 + -80x + 5xX2 + -5x2 = 0 + -400
-20X2 + -80x + 5xX2 + -5x2 = 0 + -400

Combine like terms: 0 + -400 = -400
-20X2 + -80x + 5xX2 + -5x2 = -400

Add '80x' to each side of the equation.
-20X2 + -80x + 5xX2 + 80x + -5x2 = -400 + 80x

Reorder the terms:
-20X2 + -80x + 80x + 5xX2 + -5x2 = -400 + 80x

Combine like terms: -80x + 80x = 0
-20X2 + 0 + 5xX2 + -5x2 = -400 + 80x
-20X2 + 5xX2 + -5x2 = -400 + 80x

Add '5x2' to each side of the equation.
-20X2 + 5xX2 + -5x2 + 5x2 = -400 + 80x + 5x2

Combine like terms: -5x2 + 5x2 = 0
-20X2 + 5xX2 + 0 = -400 + 80x + 5x2
-20X2 + 5xX2 = -400 + 80x + 5x2

Reorder the terms:
400 + -20X2 + -80x + 5xX2 + -5x2 = -400 + 80x + 5x2 + 400 + -80x + -5x2

Reorder the terms:
400 + -20X2 + -80x + 5xX2 + -5x2 = -400 + 400 + 80x + -80x + 5x2 + -5x2

Combine like terms: -400 + 400 = 0
400 + -20X2 + -80x + 5xX2 + -5x2 = 0 + 80x + -80x + 5x2 + -5x2
400 + -20X2 + -80x + 5xX2 + -5x2 = 80x + -80x + 5x2 + -5x2

Combine like terms: 80x + -80x = 0
400 + -20X2 + -80x + 5xX2 + -5x2 = 0 + 5x2 + -5x2
400 + -20X2 + -80x + 5xX2 + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
400 + -20X2 + -80x + 5xX2 + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(80 + -4X2 + -16x + xX2 + -1x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(80 + -4X2 + -16x + xX2 + -1x2)' equal to zero and attempt to solve:

Simplifying
80 + -4X2 + -16x + xX2 + -1x2 = 0

Solving
80 + -4X2 + -16x + xX2 + -1x2 = 0

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

Add '-80' to each side of the equation.
80 + -4X2 + -16x + xX2 + -80 + -1x2 = 0 + -80

Reorder the terms:
80 + -80 + -4X2 + -16x + xX2 + -1x2 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -4X2 + -16x + xX2 + -1x2 = 0 + -80
-4X2 + -16x + xX2 + -1x2 = 0 + -80

Combine like terms: 0 + -80 = -80
-4X2 + -16x + xX2 + -1x2 = -80

Add '16x' to each side of the equation.
-4X2 + -16x + xX2 + 16x + -1x2 = -80 + 16x

Reorder the terms:
-4X2 + -16x + 16x + xX2 + -1x2 = -80 + 16x

Combine like terms: -16x + 16x = 0
-4X2 + 0 + xX2 + -1x2 = -80 + 16x
-4X2 + xX2 + -1x2 = -80 + 16x

Add 'x2' to each side of the equation.
-4X2 + xX2 + -1x2 + x2 = -80 + 16x + x2

Combine like terms: -1x2 + x2 = 0
-4X2 + xX2 + 0 = -80 + 16x + x2
-4X2 + xX2 = -80 + 16x + x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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