x^2+20x+100=(20x+10)(20x+10)

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Solution for x^2+20x+100=(20x+10)(20x+10) equation: 


Simplifying
x2 + 20x + 100 = (20x + 10)(20x + 10)

Reorder the terms:
100 + 20x + x2 = (20x + 10)(20x + 10)

Reorder the terms:
100 + 20x + x2 = (10 + 20x)(20x + 10)

Reorder the terms:
100 + 20x + x2 = (10 + 20x)(10 + 20x)

Multiply (10 + 20x) * (10 + 20x)
100 + 20x + x2 = (10(10 + 20x) + 20x * (10 + 20x))
100 + 20x + x2 = ((10 * 10 + 20x * 10) + 20x * (10 + 20x))
100 + 20x + x2 = ((100 + 200x) + 20x * (10 + 20x))
100 + 20x + x2 = (100 + 200x + (10 * 20x + 20x * 20x))
100 + 20x + x2 = (100 + 200x + (200x + 400x2))

Combine like terms: 200x + 200x = 400x
100 + 20x + x2 = (100 + 400x + 400x2)

Add '-100' to each side of the equation.
100 + 20x + -100 + x2 = 100 + 400x + -100 + 400x2

Reorder the terms:
100 + -100 + 20x + x2 = 100 + 400x + -100 + 400x2

Combine like terms: 100 + -100 = 0
0 + 20x + x2 = 100 + 400x + -100 + 400x2
20x + x2 = 100 + 400x + -100 + 400x2

Reorder the terms:
20x + x2 = 100 + -100 + 400x + 400x2

Combine like terms: 100 + -100 = 0
20x + x2 = 0 + 400x + 400x2
20x + x2 = 400x + 400x2

Solving
20x + x2 = 400x + 400x2

Solving for variable 'x'.

Reorder the terms:
20x + -400x + x2 + -400x2 = 400x + 400x2 + -400x + -400x2

Combine like terms: 20x + -400x = -380x
-380x + x2 + -400x2 = 400x + 400x2 + -400x + -400x2

Combine like terms: x2 + -400x2 = -399x2
-380x + -399x2 = 400x + 400x2 + -400x + -400x2

Reorder the terms:
-380x + -399x2 = 400x + -400x + 400x2 + -400x2

Combine like terms: 400x + -400x = 0
-380x + -399x2 = 0 + 400x2 + -400x2
-380x + -399x2 = 400x2 + -400x2

Combine like terms: 400x2 + -400x2 = 0
-380x + -399x2 = 0

Factor out the Greatest Common Factor (GCF), '-19x'.
-19x(20 + 21x) = 0

Ignore the factor -19.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(20 + 21x)' equal to zero and attempt to solve:

Simplifying
20 + 21x = 0

Solving
20 + 21x = 0

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

Add '-20' to each side of the equation.
20 + -20 + 21x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 21x = 0 + -20
21x = 0 + -20

Combine like terms: 0 + -20 = -20
21x = -20

Divide each side by '21'.
x = -0.9523809524

Simplifying
x = -0.9523809524
Solution
x = {0, -0.9523809524}

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