16x(2x-15)=(4x+27)(x-15)

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Solution for 16x(2x-15)=(4x+27)(x-15) equation: 


Simplifying
16x(2x + -15) = (4x + 27)(x + -15)

Reorder the terms:
16x(-15 + 2x) = (4x + 27)(x + -15)
(-15 * 16x + 2x * 16x) = (4x + 27)(x + -15)
(-240x + 32x2) = (4x + 27)(x + -15)

Reorder the terms:
-240x + 32x2 = (27 + 4x)(x + -15)

Reorder the terms:
-240x + 32x2 = (27 + 4x)(-15 + x)

Multiply (27 + 4x) * (-15 + x)
-240x + 32x2 = (27(-15 + x) + 4x * (-15 + x))
-240x + 32x2 = ((-15 * 27 + x * 27) + 4x * (-15 + x))
-240x + 32x2 = ((-405 + 27x) + 4x * (-15 + x))
-240x + 32x2 = (-405 + 27x + (-15 * 4x + x * 4x))
-240x + 32x2 = (-405 + 27x + (-60x + 4x2))

Combine like terms: 27x + -60x = -33x
-240x + 32x2 = (-405 + -33x + 4x2)

Solving
-240x + 32x2 = -405 + -33x + 4x2

Solving for variable 'x'.

Reorder the terms:
405 + -240x + 33x + 32x2 + -4x2 = -405 + -33x + 4x2 + 405 + 33x + -4x2

Combine like terms: -240x + 33x = -207x
405 + -207x + 32x2 + -4x2 = -405 + -33x + 4x2 + 405 + 33x + -4x2

Combine like terms: 32x2 + -4x2 = 28x2
405 + -207x + 28x2 = -405 + -33x + 4x2 + 405 + 33x + -4x2

Reorder the terms:
405 + -207x + 28x2 = -405 + 405 + -33x + 33x + 4x2 + -4x2

Combine like terms: -405 + 405 = 0
405 + -207x + 28x2 = 0 + -33x + 33x + 4x2 + -4x2
405 + -207x + 28x2 = -33x + 33x + 4x2 + -4x2

Combine like terms: -33x + 33x = 0
405 + -207x + 28x2 = 0 + 4x2 + -4x2
405 + -207x + 28x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
405 + -207x + 28x2 = 0

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

Divide each side by '28'.
14.46428571 + -7.392857143x + x2 = 0

Move the constant term to the right:

Add '-14.46428571' to each side of the equation.
14.46428571 + -7.392857143x + -14.46428571 + x2 = 0 + -14.46428571

Reorder the terms:
14.46428571 + -14.46428571 + -7.392857143x + x2 = 0 + -14.46428571

Combine like terms: 14.46428571 + -14.46428571 = 0.00000000
0.00000000 + -7.392857143x + x2 = 0 + -14.46428571
-7.392857143x + x2 = 0 + -14.46428571

Combine like terms: 0 + -14.46428571 = -14.46428571
-7.392857143x + x2 = -14.46428571

The x term is -7.392857143x.  Take half its coefficient (-3.696428572).
Square it (13.66358419) and add it to both sides.

Add '13.66358419' to each side of the equation.
-7.392857143x + 13.66358419 + x2 = -14.46428571 + 13.66358419

Reorder the terms:
13.66358419 + -7.392857143x + x2 = -14.46428571 + 13.66358419

Combine like terms: -14.46428571 + 13.66358419 = -0.80070152
13.66358419 + -7.392857143x + x2 = -0.80070152

Factor a perfect square on the left side:
(x + -3.696428572)(x + -3.696428572) = -0.80070152

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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