(10+2x)(30+2x)=576

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Solution for (10+2x)(30+2x)=576 equation: 


Simplifying
(10 + 2x)(30 + 2x) = 576

Multiply (10 + 2x) * (30 + 2x)
(10(30 + 2x) + 2x * (30 + 2x)) = 576
((30 * 10 + 2x * 10) + 2x * (30 + 2x)) = 576
((300 + 20x) + 2x * (30 + 2x)) = 576
(300 + 20x + (30 * 2x + 2x * 2x)) = 576
(300 + 20x + (60x + 4x2)) = 576

Combine like terms: 20x + 60x = 80x
(300 + 80x + 4x2) = 576

Solving
300 + 80x + 4x2 = 576

Solving for variable 'x'.

Reorder the terms:
300 + -576 + 80x + 4x2 = 576 + -576

Combine like terms: 300 + -576 = -276
-276 + 80x + 4x2 = 576 + -576

Combine like terms: 576 + -576 = 0
-276 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-69 + 20x + x2) = 0

Factor a trinomial.
4((-23 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve:

Simplifying
-23 + -1x = 0

Solving
-23 + -1x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 0 + 23
-1x = 0 + 23

Combine like terms: 0 + 23 = 23
-1x = 23

Divide each side by '-1'.
x = -23

Simplifying
x = -23

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 = {-23, 3}

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