3000=(30-2x)(20-2x)

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Solution for 3000=(30-2x)(20-2x) equation: 


Simplifying
3000 = (30 + -2x)(20 + -2x)

Multiply (30 + -2x) * (20 + -2x)
3000 = (30(20 + -2x) + -2x * (20 + -2x))
3000 = ((20 * 30 + -2x * 30) + -2x * (20 + -2x))
3000 = ((600 + -60x) + -2x * (20 + -2x))
3000 = (600 + -60x + (20 * -2x + -2x * -2x))
3000 = (600 + -60x + (-40x + 4x2))

Combine like terms: -60x + -40x = -100x
3000 = (600 + -100x + 4x2)

Solving
3000 = 600 + -100x + 4x2

Solving for variable 'x'.

Combine like terms: 3000 + -600 = 2400
2400 + 100x + -4x2 = 600 + -100x + 4x2 + -600 + 100x + -4x2

Reorder the terms:
2400 + 100x + -4x2 = 600 + -600 + -100x + 100x + 4x2 + -4x2

Combine like terms: 600 + -600 = 0
2400 + 100x + -4x2 = 0 + -100x + 100x + 4x2 + -4x2
2400 + 100x + -4x2 = -100x + 100x + 4x2 + -4x2

Combine like terms: -100x + 100x = 0
2400 + 100x + -4x2 = 0 + 4x2 + -4x2
2400 + 100x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
2400 + 100x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(600 + 25x + -1x2) = 0

Factor a trinomial.
4((40 + -1x)(15 + x)) = 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 '(15 + x)' equal to zero and attempt to solve:

Simplifying
15 + x = 0

Solving
15 + x = 0

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

Add '-15' to each side of the equation.
15 + -15 + x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + x = 0 + -15
x = 0 + -15

Combine like terms: 0 + -15 = -15
x = -15

Simplifying
x = -15
Solution
x = {40, -15}

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