(2X-9)(8X+4)=0

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Solution for (2X-9)(8X+4)=0 equation: 


Simplifying
(2X + -9)(8X + 4) = 0

Reorder the terms:
(-9 + 2X)(8X + 4) = 0

Reorder the terms:
(-9 + 2X)(4 + 8X) = 0

Multiply (-9 + 2X) * (4 + 8X)
(-9(4 + 8X) + 2X * (4 + 8X)) = 0
((4 * -9 + 8X * -9) + 2X * (4 + 8X)) = 0
((-36 + -72X) + 2X * (4 + 8X)) = 0
(-36 + -72X + (4 * 2X + 8X * 2X)) = 0
(-36 + -72X + (8X + 16X2)) = 0

Combine like terms: -72X + 8X = -64X
(-36 + -64X + 16X2) = 0

Solving
-36 + -64X + 16X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -16X + 4X2) = 0

Factor a trinomial.
4((-1 + -2X)(9 + -2X)) = 0

Ignore the factor 4.

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

Simplifying
-1 + -2X = 0

Solving
-1 + -2X = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2X = 0 + 1

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

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

Divide each side by '-2'.
X = -0.5

Simplifying
X = -0.5

Subproblem 2
Set the factor '(9 + -2X)' equal to zero and attempt to solve:

Simplifying
9 + -2X = 0

Solving
9 + -2X = 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 + -2X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2X = 0 + -9
-2X = 0 + -9

Combine like terms: 0 + -9 = -9
-2X = -9

Divide each side by '-2'.
X = 4.5

Simplifying
X = 4.5
Solution
X = {-0.5, 4.5}

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