(8x-2)(-9x+6)=0

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Solution for (8x-2)(-9x+6)=0 equation: 


Simplifying
(8x + -2)(-9x + 6) = 0

Reorder the terms:
(-2 + 8x)(-9x + 6) = 0

Reorder the terms:
(-2 + 8x)(6 + -9x) = 0

Multiply (-2 + 8x) * (6 + -9x)
(-2(6 + -9x) + 8x * (6 + -9x)) = 0
((6 * -2 + -9x * -2) + 8x * (6 + -9x)) = 0
((-12 + 18x) + 8x * (6 + -9x)) = 0
(-12 + 18x + (6 * 8x + -9x * 8x)) = 0
(-12 + 18x + (48x + -72x2)) = 0

Combine like terms: 18x + 48x = 66x
(-12 + 66x + -72x2) = 0

Solving
-12 + 66x + -72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-2 + 11x + -12x2) = 0

Factor a trinomial.
6((-2 + 3x)(1 + -4x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-2 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 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 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

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

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

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0.6666666667, 0.25}

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