x(3x+16)=12

Solution for x(3x+16)=12 equation:

Simplifying
x(3x + 16) = 12

Reorder the terms:
x(16 + 3x) = 12
(16 * x + 3x * x) = 12
(16x + 3x2) = 12

Solving
16x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 16x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 16x + 3x2 = 0

Factor a trinomial.
(-6 + -1x)(2 + -3x) = 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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-6, 0.6666666667}