(4x+5)(5x+8)=0

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Solution for (4x+5)(5x+8)=0 equation: 


Simplifying
(4x + 5)(5x + 8) = 0

Reorder the terms:
(5 + 4x)(5x + 8) = 0

Reorder the terms:
(5 + 4x)(8 + 5x) = 0

Multiply (5 + 4x) * (8 + 5x)
(5(8 + 5x) + 4x * (8 + 5x)) = 0
((8 * 5 + 5x * 5) + 4x * (8 + 5x)) = 0
((40 + 25x) + 4x * (8 + 5x)) = 0
(40 + 25x + (8 * 4x + 5x * 4x)) = 0
(40 + 25x + (32x + 20x2)) = 0

Combine like terms: 25x + 32x = 57x
(40 + 57x + 20x2) = 0

Solving
40 + 57x + 20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + 5x)(5 + 4x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + 4x)' equal to zero and attempt to solve:

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x = 0 + -5
4x = 0 + -5

Combine like terms: 0 + -5 = -5
4x = -5

Divide each side by '4'.
x = -1.25

Simplifying
x = -1.25
Solution
x = {-1.6, -1.25}

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