(4x+1)(7x-6)=0

Solution for (4x+1)(7x-6)=0 equation:

Simplifying
(4x + 1)(7x + -6) = 0

Reorder the terms:
(1 + 4x)(7x + -6) = 0

Reorder the terms:
(1 + 4x)(-6 + 7x) = 0

Multiply (1 + 4x) * (-6 + 7x)
(1(-6 + 7x) + 4x * (-6 + 7x)) = 0
((-6 * 1 + 7x * 1) + 4x * (-6 + 7x)) = 0
((-6 + 7x) + 4x * (-6 + 7x)) = 0
(-6 + 7x + (-6 * 4x + 7x * 4x)) = 0
(-6 + 7x + (-24x + 28x2)) = 0

Combine like terms: 7x + -24x = -17x
(-6 + -17x + 28x2) = 0

Solving
-6 + -17x + 28x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -4x)(6 + -7x) = 0

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25
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 = {-0.25, 0.8571428571}