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

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


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

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

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

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

Combine like terms: -36x + 32x = -4x
(-16 + -4x + 72x2) = 0

Solving
-16 + -4x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -1x + 18x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.4444444444, 0.5}

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