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

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


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

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

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

Solving
1080 = 720 + 108x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(90 + -27x + -1x2) = 0

Factor a trinomial.
4((3 + -1x)(30 + x)) = 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 + 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
Solution
x = {3, -30}

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