(2x+3)(x+1)=(-3x-7)(x+1)

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Solution for (2x+3)(x+1)=(-3x-7)(x+1) equation: 


Simplifying
(2x + 3)(x + 1) = (-3x + -7)(x + 1)

Reorder the terms:
(3 + 2x)(x + 1) = (-3x + -7)(x + 1)

Reorder the terms:
(3 + 2x)(1 + x) = (-3x + -7)(x + 1)

Multiply (3 + 2x) * (1 + x)
(3(1 + x) + 2x * (1 + x)) = (-3x + -7)(x + 1)
((1 * 3 + x * 3) + 2x * (1 + x)) = (-3x + -7)(x + 1)
((3 + 3x) + 2x * (1 + x)) = (-3x + -7)(x + 1)
(3 + 3x + (1 * 2x + x * 2x)) = (-3x + -7)(x + 1)
(3 + 3x + (2x + 2x2)) = (-3x + -7)(x + 1)

Combine like terms: 3x + 2x = 5x
(3 + 5x + 2x2) = (-3x + -7)(x + 1)

Reorder the terms:
3 + 5x + 2x2 = (-7 + -3x)(x + 1)

Reorder the terms:
3 + 5x + 2x2 = (-7 + -3x)(1 + x)

Multiply (-7 + -3x) * (1 + x)
3 + 5x + 2x2 = (-7(1 + x) + -3x * (1 + x))
3 + 5x + 2x2 = ((1 * -7 + x * -7) + -3x * (1 + x))
3 + 5x + 2x2 = ((-7 + -7x) + -3x * (1 + x))
3 + 5x + 2x2 = (-7 + -7x + (1 * -3x + x * -3x))
3 + 5x + 2x2 = (-7 + -7x + (-3x + -3x2))

Combine like terms: -7x + -3x = -10x
3 + 5x + 2x2 = (-7 + -10x + -3x2)

Solving
3 + 5x + 2x2 = -7 + -10x + -3x2

Solving for variable 'x'.

Reorder the terms:
3 + 7 + 5x + 10x + 2x2 + 3x2 = -7 + -10x + -3x2 + 7 + 10x + 3x2

Combine like terms: 3 + 7 = 10
10 + 5x + 10x + 2x2 + 3x2 = -7 + -10x + -3x2 + 7 + 10x + 3x2

Combine like terms: 5x + 10x = 15x
10 + 15x + 2x2 + 3x2 = -7 + -10x + -3x2 + 7 + 10x + 3x2

Combine like terms: 2x2 + 3x2 = 5x2
10 + 15x + 5x2 = -7 + -10x + -3x2 + 7 + 10x + 3x2

Reorder the terms:
10 + 15x + 5x2 = -7 + 7 + -10x + 10x + -3x2 + 3x2

Combine like terms: -7 + 7 = 0
10 + 15x + 5x2 = 0 + -10x + 10x + -3x2 + 3x2
10 + 15x + 5x2 = -10x + 10x + -3x2 + 3x2

Combine like terms: -10x + 10x = 0
10 + 15x + 5x2 = 0 + -3x2 + 3x2
10 + 15x + 5x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
10 + 15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 3x + x2) = 0

Factor a trinomial.
5((2 + x)(1 + x)) = 0

Ignore the factor 5.

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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