(2x+3)(x+1)-3(x+2)(x+1)=-3(x+5)

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Solution for (2x+3)(x+1)-3(x+2)(x+1)=-3(x+5) equation: 


Simplifying
(2x + 3)(x + 1) + -3(x + 2)(x + 1) = -3(x + 5)

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

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

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

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

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

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

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

Combine like terms: 2x + 1x = 3x
3 + 5x + 2x2 + -3(2 + 3x + x2) = -3(x + 5)
3 + 5x + 2x2 + (2 * -3 + 3x * -3 + x2 * -3) = -3(x + 5)
3 + 5x + 2x2 + (-6 + -9x + -3x2) = -3(x + 5)

Reorder the terms:
3 + -6 + 5x + -9x + 2x2 + -3x2 = -3(x + 5)

Combine like terms: 3 + -6 = -3
-3 + 5x + -9x + 2x2 + -3x2 = -3(x + 5)

Combine like terms: 5x + -9x = -4x
-3 + -4x + 2x2 + -3x2 = -3(x + 5)

Combine like terms: 2x2 + -3x2 = -1x2
-3 + -4x + -1x2 = -3(x + 5)

Reorder the terms:
-3 + -4x + -1x2 = -3(5 + x)
-3 + -4x + -1x2 = (5 * -3 + x * -3)
-3 + -4x + -1x2 = (-15 + -3x)

Solving
-3 + -4x + -1x2 = -15 + -3x

Solving for variable 'x'.

Reorder the terms:
-3 + 15 + -4x + 3x + -1x2 = -15 + -3x + 15 + 3x

Combine like terms: -3 + 15 = 12
12 + -4x + 3x + -1x2 = -15 + -3x + 15 + 3x

Combine like terms: -4x + 3x = -1x
12 + -1x + -1x2 = -15 + -3x + 15 + 3x

Reorder the terms:
12 + -1x + -1x2 = -15 + 15 + -3x + 3x

Combine like terms: -15 + 15 = 0
12 + -1x + -1x2 = 0 + -3x + 3x
12 + -1x + -1x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
12 + -1x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {3, -4}

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