(10+2x)(20+2x)=600

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Solution for (10+2x)(20+2x)=600 equation: 


Simplifying
(10 + 2x)(20 + 2x) = 600

Multiply (10 + 2x) * (20 + 2x)
(10(20 + 2x) + 2x * (20 + 2x)) = 600
((20 * 10 + 2x * 10) + 2x * (20 + 2x)) = 600
((200 + 20x) + 2x * (20 + 2x)) = 600
(200 + 20x + (20 * 2x + 2x * 2x)) = 600
(200 + 20x + (40x + 4x2)) = 600

Combine like terms: 20x + 40x = 60x
(200 + 60x + 4x2) = 600

Solving
200 + 60x + 4x2 = 600

Solving for variable 'x'.

Reorder the terms:
200 + -600 + 60x + 4x2 = 600 + -600

Combine like terms: 200 + -600 = -400
-400 + 60x + 4x2 = 600 + -600

Combine like terms: 600 + -600 = 0
-400 + 60x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-100 + 15x + x2) = 0

Factor a trinomial.
4((-20 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 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 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-20, 5}

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