2x(5-6x)-12(x+3)=3x(5+4x)

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Solution for 2x(5-6x)-12(x+3)=3x(5+4x) equation: 


Simplifying
2x(5 + -6x) + -12(x + 3) = 3x(5 + 4x)
(5 * 2x + -6x * 2x) + -12(x + 3) = 3x(5 + 4x)
(10x + -12x2) + -12(x + 3) = 3x(5 + 4x)

Reorder the terms:
10x + -12x2 + -12(3 + x) = 3x(5 + 4x)
10x + -12x2 + (3 * -12 + x * -12) = 3x(5 + 4x)
10x + -12x2 + (-36 + -12x) = 3x(5 + 4x)

Reorder the terms:
-36 + 10x + -12x + -12x2 = 3x(5 + 4x)

Combine like terms: 10x + -12x = -2x
-36 + -2x + -12x2 = 3x(5 + 4x)
-36 + -2x + -12x2 = (5 * 3x + 4x * 3x)
-36 + -2x + -12x2 = (15x + 12x2)

Solving
-36 + -2x + -12x2 = 15x + 12x2

Solving for variable 'x'.

Reorder the terms:
-36 + -2x + -15x + -12x2 + -12x2 = 15x + 12x2 + -15x + -12x2

Combine like terms: -2x + -15x = -17x
-36 + -17x + -12x2 + -12x2 = 15x + 12x2 + -15x + -12x2

Combine like terms: -12x2 + -12x2 = -24x2
-36 + -17x + -24x2 = 15x + 12x2 + -15x + -12x2

Reorder the terms:
-36 + -17x + -24x2 = 15x + -15x + 12x2 + -12x2

Combine like terms: 15x + -15x = 0
-36 + -17x + -24x2 = 0 + 12x2 + -12x2
-36 + -17x + -24x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-36 + -17x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(36 + 17x + 24x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(36 + 17x + 24x2)' equal to zero and attempt to solve:

Simplifying
36 + 17x + 24x2 = 0

Solving
36 + 17x + 24x2 = 0

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

Divide each side by '24'.
1.5 + 0.7083333333x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.7083333333x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.7083333333x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.7083333333x + x2 = 0 + -1.5
0.7083333333x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.7083333333x + x2 = -1.5

The x term is 0.7083333333x.  Take half its coefficient (0.3541666667).
Square it (0.1254340278) and add it to both sides.

Add '0.1254340278' to each side of the equation.
0.7083333333x + 0.1254340278 + x2 = -1.5 + 0.1254340278

Reorder the terms:
0.1254340278 + 0.7083333333x + x2 = -1.5 + 0.1254340278

Combine like terms: -1.5 + 0.1254340278 = -1.3745659722
0.1254340278 + 0.7083333333x + x2 = -1.3745659722

Factor a perfect square on the left side:
(x + 0.3541666667)(x + 0.3541666667) = -1.3745659722

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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