442=(5+2x)*(8+3x)

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Solution for 442=(5+2x)*(8+3x) equation: 


Simplifying
442 = (5 + 2x)(8 + 3x)

Multiply (5 + 2x) * (8 + 3x)
442 = (5(8 + 3x) + 2x * (8 + 3x))
442 = ((8 * 5 + 3x * 5) + 2x * (8 + 3x))
442 = ((40 + 15x) + 2x * (8 + 3x))
442 = (40 + 15x + (8 * 2x + 3x * 2x))
442 = (40 + 15x + (16x + 6x2))

Combine like terms: 15x + 16x = 31x
442 = (40 + 31x + 6x2)

Solving
442 = 40 + 31x + 6x2

Solving for variable 'x'.

Combine like terms: 442 + -40 = 402
402 + -31x + -6x2 = 40 + 31x + 6x2 + -40 + -31x + -6x2

Reorder the terms:
402 + -31x + -6x2 = 40 + -40 + 31x + -31x + 6x2 + -6x2

Combine like terms: 40 + -40 = 0
402 + -31x + -6x2 = 0 + 31x + -31x + 6x2 + -6x2
402 + -31x + -6x2 = 31x + -31x + 6x2 + -6x2

Combine like terms: 31x + -31x = 0
402 + -31x + -6x2 = 0 + 6x2 + -6x2
402 + -31x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
402 + -31x + -6x2 = 0

Factor a trinomial.
(6 + -1x)(67 + 6x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(67 + 6x)' equal to zero and attempt to solve:

Simplifying
67 + 6x = 0

Solving
67 + 6x = 0

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

Add '-67' to each side of the equation.
67 + -67 + 6x = 0 + -67

Combine like terms: 67 + -67 = 0
0 + 6x = 0 + -67
6x = 0 + -67

Combine like terms: 0 + -67 = -67
6x = -67

Divide each side by '6'.
x = -11.16666667

Simplifying
x = -11.16666667
Solution
x = {6, -11.16666667}

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