(4x-6)(3x+1)=0

Solution for (4x-6)(3x+1)=0 equation:

Simplifying
(4x + -6)(3x + 1) = 0

Reorder the terms:
(-6 + 4x)(3x + 1) = 0

Reorder the terms:
(-6 + 4x)(1 + 3x) = 0

Multiply (-6 + 4x) * (1 + 3x)
(-6(1 + 3x) + 4x * (1 + 3x)) = 0
((1 * -6 + 3x * -6) + 4x * (1 + 3x)) = 0
((-6 + -18x) + 4x * (1 + 3x)) = 0
(-6 + -18x + (1 * 4x + 3x * 4x)) = 0
(-6 + -18x + (4x + 12x2)) = 0

Combine like terms: -18x + 4x = -14x
(-6 + -14x + 12x2) = 0

Solving
-6 + -14x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -7x + 6x2) = 0

Factor a trinomial.
2((-1 + -3x)(3 + -2x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-0.3333333333, 1.5}