(9x+4)(4x+8)=0

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Solution for (9x+4)(4x+8)=0 equation: 


Simplifying
(9x + 4)(4x + 8) = 0

Reorder the terms:
(4 + 9x)(4x + 8) = 0

Reorder the terms:
(4 + 9x)(8 + 4x) = 0

Multiply (4 + 9x) * (8 + 4x)
(4(8 + 4x) + 9x * (8 + 4x)) = 0
((8 * 4 + 4x * 4) + 9x * (8 + 4x)) = 0
((32 + 16x) + 9x * (8 + 4x)) = 0
(32 + 16x + (8 * 9x + 4x * 9x)) = 0
(32 + 16x + (72x + 36x2)) = 0

Combine like terms: 16x + 72x = 88x
(32 + 88x + 36x2) = 0

Solving
32 + 88x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 22x + 9x2) = 0

Factor a trinomial.
4((2 + x)(4 + 9x)) = 0

Ignore the factor 4.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + 9x)' equal to zero and attempt to solve:

Simplifying
4 + 9x = 0

Solving
4 + 9x = 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 + 9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9x = 0 + -4
9x = 0 + -4

Combine like terms: 0 + -4 = -4
9x = -4

Divide each side by '9'.
x = -0.4444444444

Simplifying
x = -0.4444444444
Solution
x = {-2, -0.4444444444}

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