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

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

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

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

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

Combine like terms: -3x + 24x = 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}