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

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Solution for 4(x+2)-3(x+1)=1(x+2)(x+1) equation: 


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

Reorder the terms:
4(2 + x) + -3(x + 1) = 1(x + 2)(x + 1)
(2 * 4 + x * 4) + -3(x + 1) = 1(x + 2)(x + 1)
(8 + 4x) + -3(x + 1) = 1(x + 2)(x + 1)

Reorder the terms:
8 + 4x + -3(1 + x) = 1(x + 2)(x + 1)
8 + 4x + (1 * -3 + x * -3) = 1(x + 2)(x + 1)
8 + 4x + (-3 + -3x) = 1(x + 2)(x + 1)

Reorder the terms:
8 + -3 + 4x + -3x = 1(x + 2)(x + 1)

Combine like terms: 8 + -3 = 5
5 + 4x + -3x = 1(x + 2)(x + 1)

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

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

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

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

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

Solving
5 + 1x = 2 + 3x + 1x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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


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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {1, -3}

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