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

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

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

Reorder the terms:
3x(-7 + x) = -6 + -2x
(-7 * 3x + x * 3x) = -6 + -2x
(-21x + 3x2) = -6 + -2x

Solving
-21x + 3x2 = -6 + -2x

Solving for variable 'x'.

Reorder the terms:
6 + -21x + 2x + 3x2 = -6 + -2x + 6 + 2x

Combine like terms: -21x + 2x = -19x
6 + -19x + 3x2 = -6 + -2x + 6 + 2x

Reorder the terms:
6 + -19x + 3x2 = -6 + 6 + -2x + 2x

Combine like terms: -6 + 6 = 0
6 + -19x + 3x2 = 0 + -2x + 2x
6 + -19x + 3x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + -19x + 3x2 = 0

Factor a trinomial.
(1 + -3x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {0.3333333333, 6}