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

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

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

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

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

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

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

Multiply (3 + 2x) * (4 + 5x)
6(3(4 + 5x) + 2x * (4 + 5x)) = 0
6((4 * 3 + 5x * 3) + 2x * (4 + 5x)) = 0
6((12 + 15x) + 2x * (4 + 5x)) = 0
6(12 + 15x + (4 * 2x + 5x * 2x)) = 0
6(12 + 15x + (8x + 10x2)) = 0

Combine like terms: 15x + 8x = 23x
6(12 + 23x + 10x2) = 0
(12 * 6 + 23x * 6 + 10x2 * 6) = 0
(72 + 138x + 60x2) = 0

Solving
72 + 138x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 23x + 10x2) = 0

Factor a trinomial.
6((3 + 2x)(4 + 5x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(4 + 5x)' equal to zero and attempt to solve:

Simplifying
4 + 5x = 0

Solving
4 + 5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5x = 0 + -4
5x = 0 + -4

Combine like terms: 0 + -4 = -4
5x = -4

Divide each side by '5'.
x = -0.8

Simplifying
x = -0.8
Solution
x = {-1.5, -0.8}