-5x(6x+1)=10(-2x+1)

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Solution for -5x(6x+1)=10(-2x+1) equation: 


Simplifying
-5x(6x + 1) = 10(-2x + 1)

Reorder the terms:
-5x(1 + 6x) = 10(-2x + 1)
(1 * -5x + 6x * -5x) = 10(-2x + 1)
(-5x + -30x2) = 10(-2x + 1)

Reorder the terms:
-5x + -30x2 = 10(1 + -2x)
-5x + -30x2 = (1 * 10 + -2x * 10)
-5x + -30x2 = (10 + -20x)

Solving
-5x + -30x2 = 10 + -20x

Solving for variable 'x'.

Reorder the terms:
-10 + -5x + 20x + -30x2 = 10 + -20x + -10 + 20x

Combine like terms: -5x + 20x = 15x
-10 + 15x + -30x2 = 10 + -20x + -10 + 20x

Reorder the terms:
-10 + 15x + -30x2 = 10 + -10 + -20x + 20x

Combine like terms: 10 + -10 = 0
-10 + 15x + -30x2 = 0 + -20x + 20x
-10 + 15x + -30x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
-10 + 15x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 3x + -6x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + 3x + -6x2)' equal to zero and attempt to solve:

Simplifying
-2 + 3x + -6x2 = 0

Solving
-2 + 3x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.3333333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -0.5x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -0.5x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -0.5x + x2 = 0 + -0.3333333333
-0.5x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-0.5x + x2 = -0.3333333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = -0.3333333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = -0.3333333333 + 0.0625

Combine like terms: -0.3333333333 + 0.0625 = -0.2708333333
0.0625 + -0.5x + x2 = -0.2708333333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = -0.2708333333

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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