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

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


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

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

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

Solving
2000 = 600 + 100x + 4x2

Solving for variable 'x'.

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

Reorder the terms:
1400 + -100x + -4x2 = 600 + -600 + 100x + -100x + 4x2 + -4x2

Combine like terms: 600 + -600 = 0
1400 + -100x + -4x2 = 0 + 100x + -100x + 4x2 + -4x2
1400 + -100x + -4x2 = 100x + -100x + 4x2 + -4x2

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(350 + -25x + -1x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
Set the factor '(35 + x)' equal to zero and attempt to solve:

Simplifying
35 + x = 0

Solving
35 + x = 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 + x = 0 + -35

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

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

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

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