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

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


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

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

Combine like terms: -80x + -60x = -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 + -1x2) = 0

Factor a trinomial.
4((-30 + x)(5 + -1x)) = 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 + -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 = {30, 5}

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