3(4x+1)(5x+6)=

Solution for 3(4x+1)(5x+6)= equation:

Simplifying
3(4x + 1)(5x + 6) = 0

Reorder the terms:
3(1 + 4x)(5x + 6) = 0

Reorder the terms:
3(1 + 4x)(6 + 5x) = 0

Multiply (1 + 4x) * (6 + 5x)
3(1(6 + 5x) + 4x * (6 + 5x)) = 0
3((6 * 1 + 5x * 1) + 4x * (6 + 5x)) = 0
3((6 + 5x) + 4x * (6 + 5x)) = 0
3(6 + 5x + (6 * 4x + 5x * 4x)) = 0
3(6 + 5x + (24x + 20x2)) = 0

Combine like terms: 5x + 24x = 29x
3(6 + 29x + 20x2) = 0
(6 * 3 + 29x * 3 + 20x2 * 3) = 0
(18 + 87x + 60x2) = 0

Solving
18 + 87x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 29x + 20x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + 5x)' equal to zero and attempt to solve:

Simplifying
6 + 5x = 0

Solving
6 + 5x = 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 + 5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5x = 0 + -6
5x = 0 + -6

Combine like terms: 0 + -6 = -6
5x = -6

Divide each side by '5'.
x = -1.2

Simplifying
x = -1.2
Subproblem 2
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
Solution
x = {-1.2, -0.25}