(8+2x)(10+2x)=224

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Solution for (8+2x)(10+2x)=224 equation: 


Simplifying
(8 + 2x)(10 + 2x) = 224

Multiply (8 + 2x) * (10 + 2x)
(8(10 + 2x) + 2x * (10 + 2x)) = 224
((10 * 8 + 2x * 8) + 2x * (10 + 2x)) = 224
((80 + 16x) + 2x * (10 + 2x)) = 224
(80 + 16x + (10 * 2x + 2x * 2x)) = 224
(80 + 16x + (20x + 4x2)) = 224

Combine like terms: 16x + 20x = 36x
(80 + 36x + 4x2) = 224

Solving
80 + 36x + 4x2 = 224

Solving for variable 'x'.

Reorder the terms:
80 + -224 + 36x + 4x2 = 224 + -224

Combine like terms: 80 + -224 = -144
-144 + 36x + 4x2 = 224 + -224

Combine like terms: 224 + -224 = 0
-144 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 9x + x2) = 0

Factor a trinomial.
4((-12 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12

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 = {-12, 3}

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