(4x-9)(2-x)=0

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Solution for (4x-9)(2-x)=0 equation: 


Simplifying
(4x + -9)(2 + -1x) = 0

Reorder the terms:
(-9 + 4x)(2 + -1x) = 0

Multiply (-9 + 4x) * (2 + -1x)
(-9(2 + -1x) + 4x * (2 + -1x)) = 0
((2 * -9 + -1x * -9) + 4x * (2 + -1x)) = 0
((-18 + 9x) + 4x * (2 + -1x)) = 0
(-18 + 9x + (2 * 4x + -1x * 4x)) = 0
(-18 + 9x + (8x + -4x2)) = 0

Combine like terms: 9x + 8x = 17x
(-18 + 17x + -4x2) = 0

Solving
-18 + 17x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + 4x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {2.25, 2}

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