(9x-6)(7x+4)=0

Solution for (9x-6)(7x+4)=0 equation:

Simplifying
(9x + -6)(7x + 4) = 0

Reorder the terms:
(-6 + 9x)(7x + 4) = 0

Reorder the terms:
(-6 + 9x)(4 + 7x) = 0

Multiply (-6 + 9x) * (4 + 7x)
(-6(4 + 7x) + 9x * (4 + 7x)) = 0
((4 * -6 + 7x * -6) + 9x * (4 + 7x)) = 0
((-24 + -42x) + 9x * (4 + 7x)) = 0
(-24 + -42x + (4 * 9x + 7x * 9x)) = 0
(-24 + -42x + (36x + 63x2)) = 0

Combine like terms: -42x + 36x = -6x
(-24 + -6x + 63x2) = 0

Solving
-24 + -6x + 63x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2x + 21x2) = 0

Factor a trinomial.
3((-4 + -7x)(2 + -3x)) = 0

Ignore the factor 3.
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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-0.5714285714, 0.6666666667}