(x+4)(3x+4)+5=0

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Solution for (x+4)(3x+4)+5=0 equation: 


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

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

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

Multiply (4 + x) * (4 + 3x)
(4(4 + 3x) + x(4 + 3x)) + 5 = 0
((4 * 4 + 3x * 4) + x(4 + 3x)) + 5 = 0
((16 + 12x) + x(4 + 3x)) + 5 = 0
(16 + 12x + (4 * x + 3x * x)) + 5 = 0
(16 + 12x + (4x + 3x2)) + 5 = 0

Combine like terms: 12x + 4x = 16x
(16 + 16x + 3x2) + 5 = 0

Reorder the terms:
16 + 5 + 16x + 3x2 = 0

Combine like terms: 16 + 5 = 21
21 + 16x + 3x2 = 0

Solving
21 + 16x + 3x2 = 0

Solving for variable 'x'.

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


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 '(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 = {-3, -2.333333333}

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