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

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


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

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

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

Multiply (5 + 4x) * (-4 + 5x)
(5(-4 + 5x) + 4x * (-4 + 5x)) = 0
((-4 * 5 + 5x * 5) + 4x * (-4 + 5x)) = 0
((-20 + 25x) + 4x * (-4 + 5x)) = 0
(-20 + 25x + (-4 * 4x + 5x * 4x)) = 0
(-20 + 25x + (-16x + 20x2)) = 0

Combine like terms: 25x + -16x = 9x
(-20 + 9x + 20x2) = 0

Solving
-20 + 9x + 20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
4 + -5x = 0

Solving
4 + -5x = 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 + -5x = 0 + -4

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

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

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8
Solution
x = {-1.25, 0.8}

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