(30+2x)(40+2x)=2000

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Solution for (30+2x)(40+2x)=2000 equation: 


Simplifying
(30 + 2x)(40 + 2x) = 2000

Multiply (30 + 2x) * (40 + 2x)
(30(40 + 2x) + 2x * (40 + 2x)) = 2000
((40 * 30 + 2x * 30) + 2x * (40 + 2x)) = 2000
((1200 + 60x) + 2x * (40 + 2x)) = 2000
(1200 + 60x + (40 * 2x + 2x * 2x)) = 2000
(1200 + 60x + (80x + 4x2)) = 2000

Combine like terms: 60x + 80x = 140x
(1200 + 140x + 4x2) = 2000

Solving
1200 + 140x + 4x2 = 2000

Solving for variable 'x'.

Reorder the terms:
1200 + -2000 + 140x + 4x2 = 2000 + -2000

Combine like terms: 1200 + -2000 = -800
-800 + 140x + 4x2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
-800 + 140x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-200 + 35x + x2) = 0

Factor a trinomial.
4((-40 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-40 + -1x)' equal to zero and attempt to solve:

Simplifying
-40 + -1x = 0

Solving
-40 + -1x = 0

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

Add '40' to each side of the equation.
-40 + 40 + -1x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -1x = 0 + 40
-1x = 0 + 40

Combine like terms: 0 + 40 = 40
-1x = 40

Divide each side by '-1'.
x = -40

Simplifying
x = -40

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 = {-40, 5}

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