(30-2x)(24-2x)-(30*24)=360

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Solution for (30-2x)(24-2x)-(30*24)=360 equation: 


Simplifying
(30 + -2x)(24 + -2x) + -1(30 * 24) = 360

Multiply (30 + -2x) * (24 + -2x)
(30(24 + -2x) + -2x * (24 + -2x)) + -1(30 * 24) = 360
((24 * 30 + -2x * 30) + -2x * (24 + -2x)) + -1(30 * 24) = 360
((720 + -60x) + -2x * (24 + -2x)) + -1(30 * 24) = 360
(720 + -60x + (24 * -2x + -2x * -2x)) + -1(30 * 24) = 360
(720 + -60x + (-48x + 4x2)) + -1(30 * 24) = 360

Combine like terms: -60x + -48x = -108x
(720 + -108x + 4x2) + -1(30 * 24) = 360

Multiply 30 * 24
720 + -108x + 4x2 + -1(720) = 360

Multiply -1 * 720
720 + -108x + 4x2 + -720 = 360

Reorder the terms:
720 + -720 + -108x + 4x2 = 360

Combine like terms: 720 + -720 = 0
0 + -108x + 4x2 = 360
-108x + 4x2 = 360

Solving
-108x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + -108x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + -108x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-90 + -27x + x2) = 0

Factor a trinomial.
4((-3 + -1x)(30 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 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 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Solution
x = {-3, 30}

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