40=(x+2)(3x+4)

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Solution for 40=(x+2)(3x+4) equation: 


Simplifying
40 = (x + 2)(3x + 4)

Reorder the terms:
40 = (2 + x)(3x + 4)

Reorder the terms:
40 = (2 + x)(4 + 3x)

Multiply (2 + x) * (4 + 3x)
40 = (2(4 + 3x) + x(4 + 3x))
40 = ((4 * 2 + 3x * 2) + x(4 + 3x))
40 = ((8 + 6x) + x(4 + 3x))
40 = (8 + 6x + (4 * x + 3x * x))
40 = (8 + 6x + (4x + 3x2))

Combine like terms: 6x + 4x = 10x
40 = (8 + 10x + 3x2)

Solving
40 = 8 + 10x + 3x2

Solving for variable 'x'.

Combine like terms: 40 + -8 = 32
32 + -10x + -3x2 = 8 + 10x + 3x2 + -8 + -10x + -3x2

Reorder the terms:
32 + -10x + -3x2 = 8 + -8 + 10x + -10x + 3x2 + -3x2

Combine like terms: 8 + -8 = 0
32 + -10x + -3x2 = 0 + 10x + -10x + 3x2 + -3x2
32 + -10x + -3x2 = 10x + -10x + 3x2 + -3x2

Combine like terms: 10x + -10x = 0
32 + -10x + -3x2 = 0 + 3x2 + -3x2
32 + -10x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
32 + -10x + -3x2 = 0

Factor a trinomial.
(2 + -1x)(16 + 3x) = 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 '(16 + 3x)' equal to zero and attempt to solve:

Simplifying
16 + 3x = 0

Solving
16 + 3x = 0

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

Add '-16' to each side of the equation.
16 + -16 + 3x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + 3x = 0 + -16
3x = 0 + -16

Combine like terms: 0 + -16 = -16
3x = -16

Divide each side by '3'.
x = -5.333333333

Simplifying
x = -5.333333333
Solution
x = {2, -5.333333333}

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