(x+3)(x+2)=(2x+16)(x-1)

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Solution for (x+3)(x+2)=(2x+16)(x-1) equation: 


Simplifying
(x + 3)(x + 2) = (2x + 16)(x + -1)

Reorder the terms:
(3 + x)(x + 2) = (2x + 16)(x + -1)

Reorder the terms:
(3 + x)(2 + x) = (2x + 16)(x + -1)

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) = (2x + 16)(x + -1)
((2 * 3 + x * 3) + x(2 + x)) = (2x + 16)(x + -1)
((6 + 3x) + x(2 + x)) = (2x + 16)(x + -1)
(6 + 3x + (2 * x + x * x)) = (2x + 16)(x + -1)
(6 + 3x + (2x + x2)) = (2x + 16)(x + -1)

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) = (2x + 16)(x + -1)

Reorder the terms:
6 + 5x + x2 = (16 + 2x)(x + -1)

Reorder the terms:
6 + 5x + x2 = (16 + 2x)(-1 + x)

Multiply (16 + 2x) * (-1 + x)
6 + 5x + x2 = (16(-1 + x) + 2x * (-1 + x))
6 + 5x + x2 = ((-1 * 16 + x * 16) + 2x * (-1 + x))
6 + 5x + x2 = ((-16 + 16x) + 2x * (-1 + x))
6 + 5x + x2 = (-16 + 16x + (-1 * 2x + x * 2x))
6 + 5x + x2 = (-16 + 16x + (-2x + 2x2))

Combine like terms: 16x + -2x = 14x
6 + 5x + x2 = (-16 + 14x + 2x2)

Solving
6 + 5x + x2 = -16 + 14x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + 16 + 5x + -14x + x2 + -2x2 = -16 + 14x + 2x2 + 16 + -14x + -2x2

Combine like terms: 6 + 16 = 22
22 + 5x + -14x + x2 + -2x2 = -16 + 14x + 2x2 + 16 + -14x + -2x2

Combine like terms: 5x + -14x = -9x
22 + -9x + x2 + -2x2 = -16 + 14x + 2x2 + 16 + -14x + -2x2

Combine like terms: x2 + -2x2 = -1x2
22 + -9x + -1x2 = -16 + 14x + 2x2 + 16 + -14x + -2x2

Reorder the terms:
22 + -9x + -1x2 = -16 + 16 + 14x + -14x + 2x2 + -2x2

Combine like terms: -16 + 16 = 0
22 + -9x + -1x2 = 0 + 14x + -14x + 2x2 + -2x2
22 + -9x + -1x2 = 14x + -14x + 2x2 + -2x2

Combine like terms: 14x + -14x = 0
22 + -9x + -1x2 = 0 + 2x2 + -2x2
22 + -9x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
22 + -9x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(11 + x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Solution
x = {2, -11}

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