(18+2x)(30+2x)=580

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Solution for (18+2x)(30+2x)=580 equation: 


Simplifying
(18 + 2x)(30 + 2x) = 580

Multiply (18 + 2x) * (30 + 2x)
(18(30 + 2x) + 2x * (30 + 2x)) = 580
((30 * 18 + 2x * 18) + 2x * (30 + 2x)) = 580
((540 + 36x) + 2x * (30 + 2x)) = 580
(540 + 36x + (30 * 2x + 2x * 2x)) = 580
(540 + 36x + (60x + 4x2)) = 580

Combine like terms: 36x + 60x = 96x
(540 + 96x + 4x2) = 580

Solving
540 + 96x + 4x2 = 580

Solving for variable 'x'.

Reorder the terms:
540 + -580 + 96x + 4x2 = 580 + -580

Combine like terms: 540 + -580 = -40
-40 + 96x + 4x2 = 580 + -580

Combine like terms: 580 + -580 = 0
-40 + 96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 24x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 24x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + 24x + x2 = 0

Solving
-10 + 24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 24x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 24x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 24x + x2 = 0 + 10
24x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
24x + x2 = 10

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 10 + 144

Reorder the terms:
144 + 24x + x2 = 10 + 144

Combine like terms: 10 + 144 = 154
144 + 24x + x2 = 154

Factor a perfect square on the left side:
(x + 12)(x + 12) = 154

Calculate the square root of the right side: 12.409673646

Break this problem into two subproblems by setting 
(x + 12) equal to 12.409673646 and -12.409673646.


Subproblem 1
x + 12 = 12.409673646

Simplifying
x + 12 = 12.409673646

Reorder the terms:
12 + x = 12.409673646

Solving
12 + x = 12.409673646

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = 12.409673646 + -12

Combine like terms: 12 + -12 = 0
0 + x = 12.409673646 + -12
x = 12.409673646 + -12

Combine like terms: 12.409673646 + -12 = 0.409673646
x = 0.409673646

Simplifying
x = 0.409673646


Subproblem 2
x + 12 = -12.409673646

Simplifying
x + 12 = -12.409673646

Reorder the terms:
12 + x = -12.409673646

Solving
12 + x = -12.409673646

Solving for variable 'x'.

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

Add '-12' to each side of the equation.
12 + -12 + x = -12.409673646 + -12

Combine like terms: 12 + -12 = 0
0 + x = -12.409673646 + -12
x = -12.409673646 + -12

Combine like terms: -12.409673646 + -12 = -24.409673646
x = -24.409673646

Simplifying
x = -24.409673646


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.409673646, -24.409673646}
Solution
x = {0.409673646, -24.409673646}

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