(3x-2)(x+4)=-11

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Solution for (3x-2)(x+4)=-11 equation: 


Simplifying
(3x + -2)(x + 4) = -11

Reorder the terms:
(-2 + 3x)(x + 4) = -11

Reorder the terms:
(-2 + 3x)(4 + x) = -11

Multiply (-2 + 3x) * (4 + x)
(-2(4 + x) + 3x * (4 + x)) = -11
((4 * -2 + x * -2) + 3x * (4 + x)) = -11
((-8 + -2x) + 3x * (4 + x)) = -11
(-8 + -2x + (4 * 3x + x * 3x)) = -11
(-8 + -2x + (12x + 3x2)) = -11

Combine like terms: -2x + 12x = 10x
(-8 + 10x + 3x2) = -11

Solving
-8 + 10x + 3x2 = -11

Solving for variable 'x'.

Reorder the terms:
-8 + 11 + 10x + 3x2 = -11 + 11

Combine like terms: -8 + 11 = 3
3 + 10x + 3x2 = -11 + 11

Combine like terms: -11 + 11 = 0
3 + 10x + 3x2 = 0

Factor a trinomial.
(3 + x)(1 + 3x) = 0


Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3

Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-3, -0.3333333333}

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