3(2x+4)5(x-6)=

Solution for 3(2x+4)5(x-6)= equation:

Simplifying
3(2x + 4) * 5(x + -6) = 0

Reorder the terms:
3(4 + 2x) * 5(x + -6) = 0

Reorder the terms:
3(4 + 2x) * 5(-6 + x) = 0

Reorder the terms for easier multiplication:
3 * 5(4 + 2x)(-6 + x) = 0

Multiply 3 * 5
15(4 + 2x)(-6 + x) = 0

Multiply (4 + 2x) * (-6 + x)
15(4(-6 + x) + 2x * (-6 + x)) = 0
15((-6 * 4 + x * 4) + 2x * (-6 + x)) = 0
15((-24 + 4x) + 2x * (-6 + x)) = 0
15(-24 + 4x + (-6 * 2x + x * 2x)) = 0
15(-24 + 4x + (-12x + 2x2)) = 0

Combine like terms: 4x + -12x = -8x
15(-24 + -8x + 2x2) = 0
(-24 * 15 + -8x * 15 + 2x2 * 15) = 0
(-360 + -120x + 30x2) = 0

Solving
-360 + -120x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(-12 + -4x + x2) = 0

Factor a trinomial.
30((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 30.
Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
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
Solution
x = {-2, 6}