(x+4)(5x+9)-x-4=0

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Solution for (x+4)(5x+9)-x-4=0 equation: 


Simplifying
(x + 4)(5x + 9) + -1x + -4 = 0

Reorder the terms:
(4 + x)(5x + 9) + -1x + -4 = 0

Reorder the terms:
(4 + x)(9 + 5x) + -1x + -4 = 0

Multiply (4 + x) * (9 + 5x)
(4(9 + 5x) + x(9 + 5x)) + -1x + -4 = 0
((9 * 4 + 5x * 4) + x(9 + 5x)) + -1x + -4 = 0
((36 + 20x) + x(9 + 5x)) + -1x + -4 = 0
(36 + 20x + (9 * x + 5x * x)) + -1x + -4 = 0
(36 + 20x + (9x + 5x2)) + -1x + -4 = 0

Combine like terms: 20x + 9x = 29x
(36 + 29x + 5x2) + -1x + -4 = 0

Reorder the terms:
36 + -4 + 29x + -1x + 5x2 = 0

Combine like terms: 36 + -4 = 32
32 + 29x + -1x + 5x2 = 0

Combine like terms: 29x + -1x = 28x
32 + 28x + 5x2 = 0

Solving
32 + 28x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + x)(8 + 5x) = 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 '(8 + 5x)' equal to zero and attempt to solve:

Simplifying
8 + 5x = 0

Solving
8 + 5x = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5x = 0 + -8
5x = 0 + -8

Combine like terms: 0 + -8 = -8
5x = -8

Divide each side by '5'.
x = -1.6

Simplifying
x = -1.6
Solution
x = {-4, -1.6}

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