(8x-6)(7x+1)=0

Solution for (8x-6)(7x+1)=0 equation:

Simplifying
(8x + -6)(7x + 1) = 0

Reorder the terms:
(-6 + 8x)(7x + 1) = 0

Reorder the terms:
(-6 + 8x)(1 + 7x) = 0

Multiply (-6 + 8x) * (1 + 7x)
(-6(1 + 7x) + 8x * (1 + 7x)) = 0
((1 * -6 + 7x * -6) + 8x * (1 + 7x)) = 0
((-6 + -42x) + 8x * (1 + 7x)) = 0
(-6 + -42x + (1 * 8x + 7x * 8x)) = 0
(-6 + -42x + (8x + 56x2)) = 0

Combine like terms: -42x + 8x = -34x
(-6 + -34x + 56x2) = 0

Solving
-6 + -34x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -17x + 28x2) = 0

Factor a trinomial.
2((-1 + -7x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.1428571429, 0.75}