(30+2x)(24+2x)=1080

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Solution for (30+2x)(24+2x)=1080 equation: 


Simplifying
(30 + 2x)(24 + 2x) = 1080

Multiply (30 + 2x) * (24 + 2x)
(30(24 + 2x) + 2x * (24 + 2x)) = 1080
((24 * 30 + 2x * 30) + 2x * (24 + 2x)) = 1080
((720 + 60x) + 2x * (24 + 2x)) = 1080
(720 + 60x + (24 * 2x + 2x * 2x)) = 1080
(720 + 60x + (48x + 4x2)) = 1080

Combine like terms: 60x + 48x = 108x
(720 + 108x + 4x2) = 1080

Solving
720 + 108x + 4x2 = 1080

Solving for variable 'x'.

Reorder the terms:
720 + -1080 + 108x + 4x2 = 1080 + -1080

Combine like terms: 720 + -1080 = -360
-360 + 108x + 4x2 = 1080 + -1080

Combine like terms: 1080 + -1080 = 0
-360 + 108x + 4x2 = 0

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

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-30, 3}

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