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

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


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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {2, 2.25}

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