(7x+1)(6x-2)=0

Solution for (7x+1)(6x-2)=0 equation:

Simplifying
(7x + 1)(6x + -2) = 0

Reorder the terms:
(1 + 7x)(6x + -2) = 0

Reorder the terms:
(1 + 7x)(-2 + 6x) = 0

Multiply (1 + 7x) * (-2 + 6x)
(1(-2 + 6x) + 7x * (-2 + 6x)) = 0
((-2 * 1 + 6x * 1) + 7x * (-2 + 6x)) = 0
((-2 + 6x) + 7x * (-2 + 6x)) = 0
(-2 + 6x + (-2 * 7x + 6x * 7x)) = 0
(-2 + 6x + (-14x + 42x2)) = 0

Combine like terms: 6x + -14x = -8x
(-2 + -8x + 42x2) = 0

Solving
-2 + -8x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -4x + 21x2) = 0

Factor a trinomial.
2((-1 + -7x)(1 + -3x)) = 0

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

Simplifying
-1 + -7x = 0

Solving
-1 + -7x = 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 + -7x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x = 0 + 1
-7x = 0 + 1

Combine like terms: 0 + 1 = 1
-7x = 1

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Subproblem 2
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
Solution
x = {-0.1428571429, 0.3333333333}