10=-16x^2+12x

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Solution for 10=-16x^2+12x equation: 


Simplifying
10 = -16x2 + 12x

Reorder the terms:
10 = 12x + -16x2

Solving
10 = 12x + -16x2

Solving for variable 'x'.

Reorder the terms:
10 + -12x + 16x2 = 12x + -12x + -16x2 + 16x2

Combine like terms: 12x + -12x = 0
10 + -12x + 16x2 = 0 + -16x2 + 16x2
10 + -12x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
10 + -12x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -6x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -6x + 8x2)' equal to zero and attempt to solve:

Simplifying
5 + -6x + 8x2 = 0

Solving
5 + -6x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.625 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.625' to each side of the equation.
0.625 + -0.75x + -0.625 + x2 = 0 + -0.625

Reorder the terms:
0.625 + -0.625 + -0.75x + x2 = 0 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + -0.75x + x2 = 0 + -0.625
-0.75x + x2 = 0 + -0.625

Combine like terms: 0 + -0.625 = -0.625
-0.75x + x2 = -0.625

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.625 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.625 + 0.140625

Combine like terms: -0.625 + 0.140625 = -0.484375
0.140625 + -0.75x + x2 = -0.484375

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = -0.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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