(20+2x)(30+2x)=2000

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Solution for (20+2x)(30+2x)=2000 equation: 


Simplifying
(20 + 2x)(30 + 2x) = 2000

Multiply (20 + 2x) * (30 + 2x)
(20(30 + 2x) + 2x * (30 + 2x)) = 2000
((30 * 20 + 2x * 20) + 2x * (30 + 2x)) = 2000
((600 + 40x) + 2x * (30 + 2x)) = 2000
(600 + 40x + (30 * 2x + 2x * 2x)) = 2000
(600 + 40x + (60x + 4x2)) = 2000

Combine like terms: 40x + 60x = 100x
(600 + 100x + 4x2) = 2000

Solving
600 + 100x + 4x2 = 2000

Solving for variable 'x'.

Reorder the terms:
600 + -2000 + 100x + 4x2 = 2000 + -2000

Combine like terms: 600 + -2000 = -1400
-1400 + 100x + 4x2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
-1400 + 100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-350 + 25x + x2) = 0

Factor a trinomial.
4((-35 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-35 + -1x)' equal to zero and attempt to solve:

Simplifying
-35 + -1x = 0

Solving
-35 + -1x = 0

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

Add '35' to each side of the equation.
-35 + 35 + -1x = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -1x = 0 + 35
-1x = 0 + 35

Combine like terms: 0 + 35 = 35
-1x = 35

Divide each side by '-1'.
x = -35

Simplifying
x = -35

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-35, 10}

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