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

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


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

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

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

Multiply (2 + x) * (4 + 3x)
(2(4 + 3x) + x(4 + 3x)) = (x + 2)(1 + -1x)
((4 * 2 + 3x * 2) + x(4 + 3x)) = (x + 2)(1 + -1x)
((8 + 6x) + x(4 + 3x)) = (x + 2)(1 + -1x)
(8 + 6x + (4 * x + 3x * x)) = (x + 2)(1 + -1x)
(8 + 6x + (4x + 3x2)) = (x + 2)(1 + -1x)

Combine like terms: 6x + 4x = 10x
(8 + 10x + 3x2) = (x + 2)(1 + -1x)

Reorder the terms:
8 + 10x + 3x2 = (2 + x)(1 + -1x)

Multiply (2 + x) * (1 + -1x)
8 + 10x + 3x2 = (2(1 + -1x) + x(1 + -1x))
8 + 10x + 3x2 = ((1 * 2 + -1x * 2) + x(1 + -1x))
8 + 10x + 3x2 = ((2 + -2x) + x(1 + -1x))
8 + 10x + 3x2 = (2 + -2x + (1 * x + -1x * x))
8 + 10x + 3x2 = (2 + -2x + (1x + -1x2))

Combine like terms: -2x + 1x = -1x
8 + 10x + 3x2 = (2 + -1x + -1x2)

Solving
8 + 10x + 3x2 = 2 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
8 + -2 + 10x + x + 3x2 + x2 = 2 + -1x + -1x2 + -2 + x + x2

Combine like terms: 8 + -2 = 6
6 + 10x + x + 3x2 + x2 = 2 + -1x + -1x2 + -2 + x + x2

Combine like terms: 10x + x = 11x
6 + 11x + 3x2 + x2 = 2 + -1x + -1x2 + -2 + x + x2

Combine like terms: 3x2 + x2 = 4x2
6 + 11x + 4x2 = 2 + -1x + -1x2 + -2 + x + x2

Reorder the terms:
6 + 11x + 4x2 = 2 + -2 + -1x + x + -1x2 + x2

Combine like terms: 2 + -2 = 0
6 + 11x + 4x2 = 0 + -1x + x + -1x2 + x2
6 + 11x + 4x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
6 + 11x + 4x2 = 0 + -1x2 + x2
6 + 11x + 4x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
6 + 11x + 4x2 = 0

Factor a trinomial.
(2 + x)(3 + 4x) = 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 '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-2, -0.75}

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