2x(3-5x)=4(x+3)

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Solution for 2x(3-5x)=4(x+3) equation: 


Simplifying
2x(3 + -5x) = 4(x + 3)
(3 * 2x + -5x * 2x) = 4(x + 3)
(6x + -10x2) = 4(x + 3)

Reorder the terms:
6x + -10x2 = 4(3 + x)
6x + -10x2 = (3 * 4 + x * 4)
6x + -10x2 = (12 + 4x)

Solving
6x + -10x2 = 12 + 4x

Solving for variable 'x'.

Reorder the terms:
-12 + 6x + -4x + -10x2 = 12 + 4x + -12 + -4x

Combine like terms: 6x + -4x = 2x
-12 + 2x + -10x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-12 + 2x + -10x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
-12 + 2x + -10x2 = 0 + 4x + -4x
-12 + 2x + -10x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + 2x + -10x2 = 0

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

Ignore the factor 2.

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

Simplifying
-6 + x + -5x2 = 0

Solving
-6 + x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.2 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.2x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.2x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.2x + x2 = 0 + -1.2
-0.2x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.2x + x2 = -1.2

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

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = -1.2 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = -1.2 + 0.25

Combine like terms: -1.2 + 0.25 = -0.95
0.25 + -0.2x + x2 = -0.95

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.95

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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