(6+2X)(10+2X)-60=36

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Solution for (6+2X)(10+2X)-60=36 equation: 


Simplifying
(6 + 2X)(10 + 2X) + -60 = 36

Multiply (6 + 2X) * (10 + 2X)
(6(10 + 2X) + 2X * (10 + 2X)) + -60 = 36
((10 * 6 + 2X * 6) + 2X * (10 + 2X)) + -60 = 36
((60 + 12X) + 2X * (10 + 2X)) + -60 = 36
(60 + 12X + (10 * 2X + 2X * 2X)) + -60 = 36
(60 + 12X + (20X + 4X2)) + -60 = 36

Combine like terms: 12X + 20X = 32X
(60 + 32X + 4X2) + -60 = 36

Reorder the terms:
60 + -60 + 32X + 4X2 = 36

Combine like terms: 60 + -60 = 0
0 + 32X + 4X2 = 36
32X + 4X2 = 36

Solving
32X + 4X2 = 36

Solving for variable 'X'.

Reorder the terms:
-36 + 32X + 4X2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 32X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 8X + X2) = 0

Factor a trinomial.
4((-9 + -1X)(1 + -1X)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -1X)' equal to zero and attempt to solve:

Simplifying
-9 + -1X = 0

Solving
-9 + -1X = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1X = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1X = 0 + 9
-1X = 0 + 9

Combine like terms: 0 + 9 = 9
-1X = 9

Divide each side by '-1'.
X = -9

Simplifying
X = -9

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-9, 1}

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