(x+5)(3x+4)=-8

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Solution for (x+5)(3x+4)=-8 equation: 


Simplifying
(x + 5)(3x + 4) = -8

Reorder the terms:
(5 + x)(3x + 4) = -8

Reorder the terms:
(5 + x)(4 + 3x) = -8

Multiply (5 + x) * (4 + 3x)
(5(4 + 3x) + x(4 + 3x)) = -8
((4 * 5 + 3x * 5) + x(4 + 3x)) = -8
((20 + 15x) + x(4 + 3x)) = -8
(20 + 15x + (4 * x + 3x * x)) = -8
(20 + 15x + (4x + 3x2)) = -8

Combine like terms: 15x + 4x = 19x
(20 + 19x + 3x2) = -8

Solving
20 + 19x + 3x2 = -8

Solving for variable 'x'.

Reorder the terms:
20 + 8 + 19x + 3x2 = -8 + 8

Combine like terms: 20 + 8 = 28
28 + 19x + 3x2 = -8 + 8

Combine like terms: -8 + 8 = 0
28 + 19x + 3x2 = 0

Factor a trinomial.
(4 + x)(7 + 3x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {-4, -2.333333333}

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