(x+8)(3x+4)=(x+14)(2x+3)

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Solution for (x+8)(3x+4)=(x+14)(2x+3) equation: 


Simplifying
(x + 8)(3x + 4) = (x + 14)(2x + 3)

Reorder the terms:
(8 + x)(3x + 4) = (x + 14)(2x + 3)

Reorder the terms:
(8 + x)(4 + 3x) = (x + 14)(2x + 3)

Multiply (8 + x) * (4 + 3x)
(8(4 + 3x) + x(4 + 3x)) = (x + 14)(2x + 3)
((4 * 8 + 3x * 8) + x(4 + 3x)) = (x + 14)(2x + 3)
((32 + 24x) + x(4 + 3x)) = (x + 14)(2x + 3)
(32 + 24x + (4 * x + 3x * x)) = (x + 14)(2x + 3)
(32 + 24x + (4x + 3x2)) = (x + 14)(2x + 3)

Combine like terms: 24x + 4x = 28x
(32 + 28x + 3x2) = (x + 14)(2x + 3)

Reorder the terms:
32 + 28x + 3x2 = (14 + x)(2x + 3)

Reorder the terms:
32 + 28x + 3x2 = (14 + x)(3 + 2x)

Multiply (14 + x) * (3 + 2x)
32 + 28x + 3x2 = (14(3 + 2x) + x(3 + 2x))
32 + 28x + 3x2 = ((3 * 14 + 2x * 14) + x(3 + 2x))
32 + 28x + 3x2 = ((42 + 28x) + x(3 + 2x))
32 + 28x + 3x2 = (42 + 28x + (3 * x + 2x * x))
32 + 28x + 3x2 = (42 + 28x + (3x + 2x2))

Combine like terms: 28x + 3x = 31x
32 + 28x + 3x2 = (42 + 31x + 2x2)

Solving
32 + 28x + 3x2 = 42 + 31x + 2x2

Solving for variable 'x'.

Reorder the terms:
32 + -42 + 28x + -31x + 3x2 + -2x2 = 42 + 31x + 2x2 + -42 + -31x + -2x2

Combine like terms: 32 + -42 = -10
-10 + 28x + -31x + 3x2 + -2x2 = 42 + 31x + 2x2 + -42 + -31x + -2x2

Combine like terms: 28x + -31x = -3x
-10 + -3x + 3x2 + -2x2 = 42 + 31x + 2x2 + -42 + -31x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-10 + -3x + 1x2 = 42 + 31x + 2x2 + -42 + -31x + -2x2

Reorder the terms:
-10 + -3x + 1x2 = 42 + -42 + 31x + -31x + 2x2 + -2x2

Combine like terms: 42 + -42 = 0
-10 + -3x + 1x2 = 0 + 31x + -31x + 2x2 + -2x2
-10 + -3x + 1x2 = 31x + -31x + 2x2 + -2x2

Combine like terms: 31x + -31x = 0
-10 + -3x + 1x2 = 0 + 2x2 + -2x2
-10 + -3x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + -3x + 1x2 = 0

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


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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