(18+2x)(30+2x)=1900

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Solution for (18+2x)(30+2x)=1900 equation: 


Simplifying
(18 + 2x)(30 + 2x) = 1900

Multiply (18 + 2x) * (30 + 2x)
(18(30 + 2x) + 2x * (30 + 2x)) = 1900
((30 * 18 + 2x * 18) + 2x * (30 + 2x)) = 1900
((540 + 36x) + 2x * (30 + 2x)) = 1900
(540 + 36x + (30 * 2x + 2x * 2x)) = 1900
(540 + 36x + (60x + 4x2)) = 1900

Combine like terms: 36x + 60x = 96x
(540 + 96x + 4x2) = 1900

Solving
540 + 96x + 4x2 = 1900

Solving for variable 'x'.

Reorder the terms:
540 + -1900 + 96x + 4x2 = 1900 + -1900

Combine like terms: 540 + -1900 = -1360
-1360 + 96x + 4x2 = 1900 + -1900

Combine like terms: 1900 + -1900 = 0
-1360 + 96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-340 + 24x + x2) = 0

Factor a trinomial.
4((-34 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-34 + -1x)' equal to zero and attempt to solve:

Simplifying
-34 + -1x = 0

Solving
-34 + -1x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -1x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -1x = 0 + 34
-1x = 0 + 34

Combine like terms: 0 + 34 = 34
-1x = 34

Divide each side by '-1'.
x = -34

Simplifying
x = -34

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-34, 10}

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