(x+6)(3x+4)=-11

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Solution for (x+6)(3x+4)=-11 equation: 


Simplifying
(x + 6)(3x + 4) = -11

Reorder the terms:
(6 + x)(3x + 4) = -11

Reorder the terms:
(6 + x)(4 + 3x) = -11

Multiply (6 + x) * (4 + 3x)
(6(4 + 3x) + x(4 + 3x)) = -11
((4 * 6 + 3x * 6) + x(4 + 3x)) = -11
((24 + 18x) + x(4 + 3x)) = -11
(24 + 18x + (4 * x + 3x * x)) = -11
(24 + 18x + (4x + 3x2)) = -11

Combine like terms: 18x + 4x = 22x
(24 + 22x + 3x2) = -11

Solving
24 + 22x + 3x2 = -11

Solving for variable 'x'.

Reorder the terms:
24 + 11 + 22x + 3x2 = -11 + 11

Combine like terms: 24 + 11 = 35
35 + 22x + 3x2 = -11 + 11

Combine like terms: -11 + 11 = 0
35 + 22x + 3x2 = 0

Factor a trinomial.
(5 + x)(7 + 3x) = 0


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

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 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 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {-5, -2.333333333}

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