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

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

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

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

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

Multiply (-6 + 7x) * (4 + 7x)
4(-6(4 + 7x) + 7x * (4 + 7x)) = 0
4((4 * -6 + 7x * -6) + 7x * (4 + 7x)) = 0
4((-24 + -42x) + 7x * (4 + 7x)) = 0
4(-24 + -42x + (4 * 7x + 7x * 7x)) = 0
4(-24 + -42x + (28x + 49x2)) = 0

Combine like terms: -42x + 28x = -14x
4(-24 + -14x + 49x2) = 0
(-24 * 4 + -14x * 4 + 49x2 * 4) = 0
(-96 + -56x + 196x2) = 0

Solving
-96 + -56x + 196x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -14x + 49x2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

Solving
-4 + -7x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7x = 0 + 4
-7x = 0 + 4

Combine like terms: 0 + 4 = 4
-7x = 4

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714
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 = {-0.5714285714, 0.8571428571}