(4x+3)(2x+6)=0

Solution for (4x+3)(2x+6)=0 equation:

Simplifying
(4x + 3)(2x + 6) = 0

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

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

Multiply (3 + 4x) * (6 + 2x)
(3(6 + 2x) + 4x * (6 + 2x)) = 0
((6 * 3 + 2x * 3) + 4x * (6 + 2x)) = 0
((18 + 6x) + 4x * (6 + 2x)) = 0
(18 + 6x + (6 * 4x + 2x * 4x)) = 0
(18 + 6x + (24x + 8x2)) = 0

Combine like terms: 6x + 24x = 30x
(18 + 30x + 8x2) = 0

Solving
18 + 30x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 15x + 4x2) = 0

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

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
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 = {-3, -0.75}