600=(30+2x)(40+2x)

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Solution for 600=(30+2x)(40+2x) equation: 


Simplifying
600 = (30 + 2x)(40 + 2x)

Multiply (30 + 2x) * (40 + 2x)
600 = (30(40 + 2x) + 2x * (40 + 2x))
600 = ((40 * 30 + 2x * 30) + 2x * (40 + 2x))
600 = ((1200 + 60x) + 2x * (40 + 2x))
600 = (1200 + 60x + (40 * 2x + 2x * 2x))
600 = (1200 + 60x + (80x + 4x2))

Combine like terms: 60x + 80x = 140x
600 = (1200 + 140x + 4x2)

Solving
600 = 1200 + 140x + 4x2

Solving for variable 'x'.

Combine like terms: 600 + -1200 = -600
-600 + -140x + -4x2 = 1200 + 140x + 4x2 + -1200 + -140x + -4x2

Reorder the terms:
-600 + -140x + -4x2 = 1200 + -1200 + 140x + -140x + 4x2 + -4x2

Combine like terms: 1200 + -1200 = 0
-600 + -140x + -4x2 = 0 + 140x + -140x + 4x2 + -4x2
-600 + -140x + -4x2 = 140x + -140x + 4x2 + -4x2

Combine like terms: 140x + -140x = 0
-600 + -140x + -4x2 = 0 + 4x2 + -4x2
-600 + -140x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-600 + -140x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(150 + 35x + x2) = 0

Factor a trinomial.
-4((30 + x)(5 + x)) = 0

Ignore the factor -4.

Subproblem 1
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x = 0 + -30
x = 0 + -30

Combine like terms: 0 + -30 = -30
x = -30

Simplifying
x = -30

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

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {-30, -5}

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