(2x-6)(4x+1)=0

Solution for (2x-6)(4x+1)=0 equation:

Simplifying
(2x + -6)(4x + 1) = 0

Reorder the terms:
(-6 + 2x)(4x + 1) = 0

Reorder the terms:
(-6 + 2x)(1 + 4x) = 0

Multiply (-6 + 2x) * (1 + 4x)
(-6(1 + 4x) + 2x * (1 + 4x)) = 0
((1 * -6 + 4x * -6) + 2x * (1 + 4x)) = 0
((-6 + -24x) + 2x * (1 + 4x)) = 0
(-6 + -24x + (1 * 2x + 4x * 2x)) = 0
(-6 + -24x + (2x + 8x2)) = 0

Combine like terms: -24x + 2x = -22x
(-6 + -22x + 8x2) = 0

Solving
-6 + -22x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -11x + 4x2) = 0

Factor a trinomial.
2((-1 + -4x)(3 + -1x)) = 0

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

Simplifying
3 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.25, 3}