(5x-8)(9x-10)=0

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Solution for (5x-8)(9x-10)=0 equation: 


Simplifying
(5x + -8)(9x + -10) = 0

Reorder the terms:
(-8 + 5x)(9x + -10) = 0

Reorder the terms:
(-8 + 5x)(-10 + 9x) = 0

Multiply (-8 + 5x) * (-10 + 9x)
(-8(-10 + 9x) + 5x * (-10 + 9x)) = 0
((-10 * -8 + 9x * -8) + 5x * (-10 + 9x)) = 0
((80 + -72x) + 5x * (-10 + 9x)) = 0
(80 + -72x + (-10 * 5x + 9x * 5x)) = 0
(80 + -72x + (-50x + 45x2)) = 0

Combine like terms: -72x + -50x = -122x
(80 + -122x + 45x2) = 0

Solving
80 + -122x + 45x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + -9x)(8 + -5x) = 0


Subproblem 1
Set the factor '(10 + -9x)' equal to zero and attempt to solve:

Simplifying
10 + -9x = 0

Solving
10 + -9x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -9x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9x = 0 + -10
-9x = 0 + -10

Combine like terms: 0 + -10 = -10
-9x = -10

Divide each side by '-9'.
x = 1.111111111

Simplifying
x = 1.111111111

Subproblem 2
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
Solution
x = {1.111111111, 1.6}

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