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

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

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

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

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

Multiply (-6 + 7x) * (1 + 2x)
(-6(1 + 2x) + 7x * (1 + 2x)) = 0
((1 * -6 + 2x * -6) + 7x * (1 + 2x)) = 0
((-6 + -12x) + 7x * (1 + 2x)) = 0
(-6 + -12x + (1 * 7x + 2x * 7x)) = 0
(-6 + -12x + (7x + 14x2)) = 0

Combine like terms: -12x + 7x = -5x
(-6 + -5x + 14x2) = 0

Solving
-6 + -5x + 14x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5
Subproblem 2
Set the factor '(6 + -7x)' equal to zero and attempt to solve:

Simplifying
6 + -7x = 0

Solving
6 + -7x = 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 + -7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x = 0 + -6
-7x = 0 + -6

Combine like terms: 0 + -6 = -6
-7x = -6

Divide each side by '-7'.
x = 0.8571428571

Simplifying
x = 0.8571428571
Solution
x = {-0.5, 0.8571428571}