6(2-7x)+x(7x-2)=0

Solution for 6(2-7x)+x(7x-2)=0 equation:

Simplifying
6(2 + -7x) + x(7x + -2) = 0
(2 * 6 + -7x * 6) + x(7x + -2) = 0
(12 + -42x) + x(7x + -2) = 0

Reorder the terms:
12 + -42x + x(-2 + 7x) = 0
12 + -42x + (-2 * x + 7x * x) = 0
12 + -42x + (-2x + 7x2) = 0

Combine like terms: -42x + -2x = -44x
12 + -44x + 7x2 = 0

Solving
12 + -44x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -7x)(6 + -1x) = 0

Subproblem 1
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
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 = {0.2857142857, 6}