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

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


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

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

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

Multiply (-4 + 9x) * (8 + 2x)
(-4(8 + 2x) + 9x * (8 + 2x)) = 0
((8 * -4 + 2x * -4) + 9x * (8 + 2x)) = 0
((-32 + -8x) + 9x * (8 + 2x)) = 0
(-32 + -8x + (8 * 9x + 2x * 9x)) = 0
(-32 + -8x + (72x + 18x2)) = 0

Combine like terms: -8x + 72x = 64x
(-32 + 64x + 18x2) = 0

Solving
-32 + 64x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 32x + 9x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444
Solution
x = {-4, 0.4444444444}

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