4(5x-3)(6+x)=0

Solution for 4(5x-3)(6+x)=0 equation:

Simplifying
4(5x + -3)(6 + x) = 0

Reorder the terms:
4(-3 + 5x)(6 + x) = 0

Multiply (-3 + 5x) * (6 + x)
4(-3(6 + x) + 5x * (6 + x)) = 0
4((6 * -3 + x * -3) + 5x * (6 + x)) = 0
4((-18 + -3x) + 5x * (6 + x)) = 0
4(-18 + -3x + (6 * 5x + x * 5x)) = 0
4(-18 + -3x + (30x + 5x2)) = 0

Combine like terms: -3x + 30x = 27x
4(-18 + 27x + 5x2) = 0
(-18 * 4 + 27x * 4 + 5x2 * 4) = 0
(-72 + 108x + 20x2) = 0

Solving
-72 + 108x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + 27x + 5x2) = 0

Factor a trinomial.
4((-6 + -1x)(3 + -5x)) = 0

Ignore the factor 4.
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 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-6, 0.6}