(2x+7)(3x+8)=6

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Solution for (2x+7)(3x+8)=6 equation:


Simplifying
(2x + 7)(3x + 8) = 6

Reorder the terms:
(7 + 2x)(3x + 8) = 6

Reorder the terms:
(7 + 2x)(8 + 3x) = 6

Multiply (7 + 2x) * (8 + 3x)
(7(8 + 3x) + 2x * (8 + 3x)) = 6
((8 * 7 + 3x * 7) + 2x * (8 + 3x)) = 6
((56 + 21x) + 2x * (8 + 3x)) = 6
(56 + 21x + (8 * 2x + 3x * 2x)) = 6
(56 + 21x + (16x + 6x2)) = 6

Combine like terms: 21x + 16x = 37x
(56 + 37x + 6x2) = 6

Solving
56 + 37x + 6x2 = 6

Solving for variable 'x'.

Reorder the terms:
56 + -6 + 37x + 6x2 = 6 + -6

Combine like terms: 56 + -6 = 50
50 + 37x + 6x2 = 6 + -6

Combine like terms: 6 + -6 = 0
50 + 37x + 6x2 = 0

Factor a trinomial.
(25 + 6x)(2 + x) = 0


Subproblem 1
Set the factor '(25 + 6x)' equal to zero and attempt to solve:

Simplifying
25 + 6x = 0

Solving
25 + 6x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 6x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 6x = 0 + -25
6x = 0 + -25

Combine like terms: 0 + -25 = -25
6x = -25

Divide each side by '6'.
x = -4.166666667

Simplifying
x = -4.166666667

Subproblem 2
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
Solution
x = {-4.166666667, -2}

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