(4x-9)(8x-4)=0

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Solution for (4x-9)(8x-4)=0 equation: 


Simplifying
(4x + -9)(8x + -4) = 0

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

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

Multiply (-9 + 4x) * (-4 + 8x)
(-9(-4 + 8x) + 4x * (-4 + 8x)) = 0
((-4 * -9 + 8x * -9) + 4x * (-4 + 8x)) = 0
((36 + -72x) + 4x * (-4 + 8x)) = 0
(36 + -72x + (-4 * 4x + 8x * 4x)) = 0
(36 + -72x + (-16x + 32x2)) = 0

Combine like terms: -72x + -16x = -88x
(36 + -88x + 32x2) = 0

Solving
36 + -88x + 32x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -22x + 8x2) = 0

Factor a trinomial.
4((1 + -2x)(9 + -4x)) = 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 + -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 = {0.5, 2.25}

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