(x+2)(2x+3)=(x+2)(x+2)

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


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

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

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

Multiply (2 + x) * (3 + 2x)
(2(3 + 2x) + x(3 + 2x)) = (x + 2)(x + 2)
((3 * 2 + 2x * 2) + x(3 + 2x)) = (x + 2)(x + 2)
((6 + 4x) + x(3 + 2x)) = (x + 2)(x + 2)
(6 + 4x + (3 * x + 2x * x)) = (x + 2)(x + 2)
(6 + 4x + (3x + 2x2)) = (x + 2)(x + 2)

Combine like terms: 4x + 3x = 7x
(6 + 7x + 2x2) = (x + 2)(x + 2)

Reorder the terms:
6 + 7x + 2x2 = (2 + x)(x + 2)

Reorder the terms:
6 + 7x + 2x2 = (2 + x)(2 + x)

Multiply (2 + x) * (2 + x)
6 + 7x + 2x2 = (2(2 + x) + x(2 + x))
6 + 7x + 2x2 = ((2 * 2 + x * 2) + x(2 + x))
6 + 7x + 2x2 = ((4 + 2x) + x(2 + x))
6 + 7x + 2x2 = (4 + 2x + (2 * x + x * x))
6 + 7x + 2x2 = (4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
6 + 7x + 2x2 = (4 + 4x + x2)

Solving
6 + 7x + 2x2 = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
6 + -4 + 7x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 6 + -4 = 2
2 + 7x + -4x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 7x + -4x = 3x
2 + 3x + 2x2 + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
2 + 3x + 1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
2 + 3x + 1x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
2 + 3x + 1x2 = 0 + 4x + -4x + x2 + -1x2
2 + 3x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
2 + 3x + 1x2 = 0 + x2 + -1x2
2 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + 3x + 1x2 = 0

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


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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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