(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 = 7x
(-40 + 7x + 20x2) = 0

Solving
-40 + 7x + 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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