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

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

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

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

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

Multiply (6 + x) * (-3 + 4x)
(6(-3 + 4x) + x(-3 + 4x)) = 0
((-3 * 6 + 4x * 6) + x(-3 + 4x)) = 0
((-18 + 24x) + x(-3 + 4x)) = 0
(-18 + 24x + (-3 * x + 4x * x)) = 0
(-18 + 24x + (-3x + 4x2)) = 0

Combine like terms: 24x + -3x = 21x
(-18 + 21x + 4x2) = 0

Solving
-18 + 21x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(3 + -4x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-6, 0.75}