(3x+2)(x+3)=(2x-3)(x+14)

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Solution for (3x+2)(x+3)=(2x-3)(x+14) equation: 


Simplifying
(3x + 2)(x + 3) = (2x + -3)(x + 14)

Reorder the terms:
(2 + 3x)(x + 3) = (2x + -3)(x + 14)

Reorder the terms:
(2 + 3x)(3 + x) = (2x + -3)(x + 14)

Multiply (2 + 3x) * (3 + x)
(2(3 + x) + 3x * (3 + x)) = (2x + -3)(x + 14)
((3 * 2 + x * 2) + 3x * (3 + x)) = (2x + -3)(x + 14)
((6 + 2x) + 3x * (3 + x)) = (2x + -3)(x + 14)
(6 + 2x + (3 * 3x + x * 3x)) = (2x + -3)(x + 14)
(6 + 2x + (9x + 3x2)) = (2x + -3)(x + 14)

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2) = (2x + -3)(x + 14)

Reorder the terms:
6 + 11x + 3x2 = (-3 + 2x)(x + 14)

Reorder the terms:
6 + 11x + 3x2 = (-3 + 2x)(14 + x)

Multiply (-3 + 2x) * (14 + x)
6 + 11x + 3x2 = (-3(14 + x) + 2x * (14 + x))
6 + 11x + 3x2 = ((14 * -3 + x * -3) + 2x * (14 + x))
6 + 11x + 3x2 = ((-42 + -3x) + 2x * (14 + x))
6 + 11x + 3x2 = (-42 + -3x + (14 * 2x + x * 2x))
6 + 11x + 3x2 = (-42 + -3x + (28x + 2x2))

Combine like terms: -3x + 28x = 25x
6 + 11x + 3x2 = (-42 + 25x + 2x2)

Solving
6 + 11x + 3x2 = -42 + 25x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + 42 + 11x + -25x + 3x2 + -2x2 = -42 + 25x + 2x2 + 42 + -25x + -2x2

Combine like terms: 6 + 42 = 48
48 + 11x + -25x + 3x2 + -2x2 = -42 + 25x + 2x2 + 42 + -25x + -2x2

Combine like terms: 11x + -25x = -14x
48 + -14x + 3x2 + -2x2 = -42 + 25x + 2x2 + 42 + -25x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
48 + -14x + 1x2 = -42 + 25x + 2x2 + 42 + -25x + -2x2

Reorder the terms:
48 + -14x + 1x2 = -42 + 42 + 25x + -25x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
48 + -14x + 1x2 = 0 + 25x + -25x + 2x2 + -2x2
48 + -14x + 1x2 = 25x + -25x + 2x2 + -2x2

Combine like terms: 25x + -25x = 0
48 + -14x + 1x2 = 0 + 2x2 + -2x2
48 + -14x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
48 + -14x + 1x2 = 0

Factor a trinomial.
(6 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {6, 8}

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