(5x+4)(6+x)=0

Solution for (5x+4)(6+x)=0 equation:

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

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

Multiply (4 + 5x) * (6 + x)
(4(6 + x) + 5x * (6 + x)) = 0
((6 * 4 + x * 4) + 5x * (6 + x)) = 0
((24 + 4x) + 5x * (6 + x)) = 0
(24 + 4x + (6 * 5x + x * 5x)) = 0
(24 + 4x + (30x + 5x2)) = 0

Combine like terms: 4x + 30x = 34x
(24 + 34x + 5x2) = 0

Solving
24 + 34x + 5x2 = 0

Solving for variable 'x'.

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

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

Simplifying
6 + x = 0

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

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

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

Simplifying
x = -6
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 = {-6, -0.8}