8x=12x(x-.5)

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Solution for 8x=12x(x-.5) equation: 


Simplifying
8x = 12x(x + -0.5)

Reorder the terms:
8x = 12x(-0.5 + x)
8x = (-0.5 * 12x + x * 12x)
8x = (-6x + 12x2)

Solving
8x = -6x + 12x2

Solving for variable 'x'.

Combine like terms: 8x + 6x = 14x
14x + -12x2 = -6x + 12x2 + 6x + -12x2

Reorder the terms:
14x + -12x2 = -6x + 6x + 12x2 + -12x2

Combine like terms: -6x + 6x = 0
14x + -12x2 = 0 + 12x2 + -12x2
14x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
14x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + -6x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {0, 1.166666667}

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