(5x-2)(9-x)=0

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Solution for (5x-2)(9-x)=0 equation: 


Simplifying
(5x + -2)(9 + -1x) = 0

Reorder the terms:
(-2 + 5x)(9 + -1x) = 0

Multiply (-2 + 5x) * (9 + -1x)
(-2(9 + -1x) + 5x * (9 + -1x)) = 0
((9 * -2 + -1x * -2) + 5x * (9 + -1x)) = 0
((-18 + 2x) + 5x * (9 + -1x)) = 0
(-18 + 2x + (9 * 5x + -1x * 5x)) = 0
(-18 + 2x + (45x + -5x2)) = 0

Combine like terms: 2x + 45x = 47x
(-18 + 47x + -5x2) = 0

Solving
-18 + 47x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + x)(2 + -5x) = 0


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

Simplifying
-9 + x = 0

Solving
-9 + x = 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 + x = 0 + 9

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

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

Simplifying
x = 9

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

Simplifying
2 + -5x = 0

Solving
2 + -5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {9, 0.4}

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