(2X+3)(X+2)=66

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Solution for (2X+3)(X+2)=66 equation: 


Simplifying
(2X + 3)(X + 2) = 66

Reorder the terms:
(3 + 2X)(X + 2) = 66

Reorder the terms:
(3 + 2X)(2 + X) = 66

Multiply (3 + 2X) * (2 + X)
(3(2 + X) + 2X * (2 + X)) = 66
((2 * 3 + X * 3) + 2X * (2 + X)) = 66
((6 + 3X) + 2X * (2 + X)) = 66
(6 + 3X + (2 * 2X + X * 2X)) = 66
(6 + 3X + (4X + 2X2)) = 66

Combine like terms: 3X + 4X = 7X
(6 + 7X + 2X2) = 66

Solving
6 + 7X + 2X2 = 66

Solving for variable 'X'.

Reorder the terms:
6 + -66 + 7X + 2X2 = 66 + -66

Combine like terms: 6 + -66 = -60
-60 + 7X + 2X2 = 66 + -66

Combine like terms: 66 + -66 = 0
-60 + 7X + 2X2 = 0

Factor a trinomial.
(-15 + -2X)(4 + -1X) = 0


Subproblem 1
Set the factor '(-15 + -2X)' equal to zero and attempt to solve:

Simplifying
-15 + -2X = 0

Solving
-15 + -2X = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2X = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2X = 0 + 15
-2X = 0 + 15

Combine like terms: 0 + 15 = 15
-2X = 15

Divide each side by '-2'.
X = -7.5

Simplifying
X = -7.5

Subproblem 2
Set the factor '(4 + -1X)' equal to zero and attempt to solve:

Simplifying
4 + -1X = 0

Solving
4 + -1X = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1X = 0 + -4
-1X = 0 + -4

Combine like terms: 0 + -4 = -4
-1X = -4

Divide each side by '-1'.
X = 4

Simplifying
X = 4
Solution
X = {-7.5, 4}

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