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

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

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

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

Reorder the terms:
-21x + 6x2 = 2(3 + 7x)
-21x + 6x2 = (3 * 2 + 7x * 2)
-21x + 6x2 = (6 + 14x)

Solving
-21x + 6x2 = 6 + 14x

Solving for variable 'x'.

Reorder the terms:
-6 + -21x + -14x + 6x2 = 6 + 14x + -6 + -14x

Combine like terms: -21x + -14x = -35x
-6 + -35x + 6x2 = 6 + 14x + -6 + -14x

Reorder the terms:
-6 + -35x + 6x2 = 6 + -6 + 14x + -14x

Combine like terms: 6 + -6 = 0
-6 + -35x + 6x2 = 0 + 14x + -14x
-6 + -35x + 6x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-6 + -35x + 6x2 = 0

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

Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

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

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

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
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 = {-0.1666666667, 6}