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

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

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

Reorder the terms:
2x(7 + 3x) = x + -6
(7 * 2x + 3x * 2x) = x + -6
(14x + 6x2) = x + -6

Reorder the terms:
14x + 6x2 = -6 + x

Solving
14x + 6x2 = -6 + x

Solving for variable 'x'.

Reorder the terms:
6 + 14x + -1x + 6x2 = -6 + x + 6 + -1x

Combine like terms: 14x + -1x = 13x
6 + 13x + 6x2 = -6 + x + 6 + -1x

Reorder the terms:
6 + 13x + 6x2 = -6 + 6 + x + -1x

Combine like terms: -6 + 6 = 0
6 + 13x + 6x2 = 0 + x + -1x
6 + 13x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 13x + 6x2 = 0

Factor a trinomial.
(3 + 2x)(2 + 3x) = 0

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

Simplifying
3 + 2x = 0

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

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, -0.6666666667}