(x+1)(4x+6)=0

Solution for (x+1)(4x+6)=0 equation:

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

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

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

Multiply (1 + x) * (6 + 4x)
(1(6 + 4x) + x(6 + 4x)) = 0
((6 * 1 + 4x * 1) + x(6 + 4x)) = 0
((6 + 4x) + x(6 + 4x)) = 0
(6 + 4x + (6 * x + 4x * x)) = 0
(6 + 4x + (6x + 4x2)) = 0

Combine like terms: 4x + 6x = 10x
(6 + 10x + 4x2) = 0

Solving
6 + 10x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 5x + 2x2) = 0

Factor a trinomial.
2((3 + 2x)(1 + x)) = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-1.5, -1}