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

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


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

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

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

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

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

Solving
-20 + -9x + 20x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {-0.8, 1.25}

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