(3x+4)(x+8)=(x+18)(2x+1)

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Solution for (3x+4)(x+8)=(x+18)(2x+1) equation: 


Simplifying
(3x + 4)(x + 8) = (x + 18)(2x + 1)

Reorder the terms:
(4 + 3x)(x + 8) = (x + 18)(2x + 1)

Reorder the terms:
(4 + 3x)(8 + x) = (x + 18)(2x + 1)

Multiply (4 + 3x) * (8 + x)
(4(8 + x) + 3x * (8 + x)) = (x + 18)(2x + 1)
((8 * 4 + x * 4) + 3x * (8 + x)) = (x + 18)(2x + 1)
((32 + 4x) + 3x * (8 + x)) = (x + 18)(2x + 1)
(32 + 4x + (8 * 3x + x * 3x)) = (x + 18)(2x + 1)
(32 + 4x + (24x + 3x2)) = (x + 18)(2x + 1)

Combine like terms: 4x + 24x = 28x
(32 + 28x + 3x2) = (x + 18)(2x + 1)

Reorder the terms:
32 + 28x + 3x2 = (18 + x)(2x + 1)

Reorder the terms:
32 + 28x + 3x2 = (18 + x)(1 + 2x)

Multiply (18 + x) * (1 + 2x)
32 + 28x + 3x2 = (18(1 + 2x) + x(1 + 2x))
32 + 28x + 3x2 = ((1 * 18 + 2x * 18) + x(1 + 2x))
32 + 28x + 3x2 = ((18 + 36x) + x(1 + 2x))
32 + 28x + 3x2 = (18 + 36x + (1 * x + 2x * x))
32 + 28x + 3x2 = (18 + 36x + (1x + 2x2))

Combine like terms: 36x + 1x = 37x
32 + 28x + 3x2 = (18 + 37x + 2x2)

Solving
32 + 28x + 3x2 = 18 + 37x + 2x2

Solving for variable 'x'.

Reorder the terms:
32 + -18 + 28x + -37x + 3x2 + -2x2 = 18 + 37x + 2x2 + -18 + -37x + -2x2

Combine like terms: 32 + -18 = 14
14 + 28x + -37x + 3x2 + -2x2 = 18 + 37x + 2x2 + -18 + -37x + -2x2

Combine like terms: 28x + -37x = -9x
14 + -9x + 3x2 + -2x2 = 18 + 37x + 2x2 + -18 + -37x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
14 + -9x + 1x2 = 18 + 37x + 2x2 + -18 + -37x + -2x2

Reorder the terms:
14 + -9x + 1x2 = 18 + -18 + 37x + -37x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
14 + -9x + 1x2 = 0 + 37x + -37x + 2x2 + -2x2
14 + -9x + 1x2 = 37x + -37x + 2x2 + -2x2

Combine like terms: 37x + -37x = 0
14 + -9x + 1x2 = 0 + 2x2 + -2x2
14 + -9x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
14 + -9x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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