(x-5)(4x-9)=0

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Solution for (x-5)(4x-9)=0 equation: 


Simplifying
(x + -5)(4x + -9) = 0

Reorder the terms:
(-5 + x)(4x + -9) = 0

Reorder the terms:
(-5 + x)(-9 + 4x) = 0

Multiply (-5 + x) * (-9 + 4x)
(-5(-9 + 4x) + x(-9 + 4x)) = 0
((-9 * -5 + 4x * -5) + x(-9 + 4x)) = 0
((45 + -20x) + x(-9 + 4x)) = 0
(45 + -20x + (-9 * x + 4x * x)) = 0
(45 + -20x + (-9x + 4x2)) = 0

Combine like terms: -20x + -9x = -29x
(45 + -29x + 4x2) = 0

Solving
45 + -29x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(9 + -4x)(5 + -1x) = 0


Subproblem 1
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2.25, 5}

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