(3x+4)(6x+7)-5=(6x-7)(2x+5)

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Solution for (3x+4)(6x+7)-5=(6x-7)(2x+5) equation:


Simplifying
(3x + 4)(6x + 7) + -5 = (6x + -7)(2x + 5)

Reorder the terms:
(4 + 3x)(6x + 7) + -5 = (6x + -7)(2x + 5)

Reorder the terms:
(4 + 3x)(7 + 6x) + -5 = (6x + -7)(2x + 5)

Multiply (4 + 3x) * (7 + 6x)
(4(7 + 6x) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5)
((7 * 4 + 6x * 4) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5)
((28 + 24x) + 3x * (7 + 6x)) + -5 = (6x + -7)(2x + 5)
(28 + 24x + (7 * 3x + 6x * 3x)) + -5 = (6x + -7)(2x + 5)
(28 + 24x + (21x + 18x2)) + -5 = (6x + -7)(2x + 5)

Combine like terms: 24x + 21x = 45x
(28 + 45x + 18x2) + -5 = (6x + -7)(2x + 5)

Reorder the terms:
28 + -5 + 45x + 18x2 = (6x + -7)(2x + 5)

Combine like terms: 28 + -5 = 23
23 + 45x + 18x2 = (6x + -7)(2x + 5)

Reorder the terms:
23 + 45x + 18x2 = (-7 + 6x)(2x + 5)

Reorder the terms:
23 + 45x + 18x2 = (-7 + 6x)(5 + 2x)

Multiply (-7 + 6x) * (5 + 2x)
23 + 45x + 18x2 = (-7(5 + 2x) + 6x * (5 + 2x))
23 + 45x + 18x2 = ((5 * -7 + 2x * -7) + 6x * (5 + 2x))
23 + 45x + 18x2 = ((-35 + -14x) + 6x * (5 + 2x))
23 + 45x + 18x2 = (-35 + -14x + (5 * 6x + 2x * 6x))
23 + 45x + 18x2 = (-35 + -14x + (30x + 12x2))

Combine like terms: -14x + 30x = 16x
23 + 45x + 18x2 = (-35 + 16x + 12x2)

Solving
23 + 45x + 18x2 = -35 + 16x + 12x2

Solving for variable 'x'.

Reorder the terms:
23 + 35 + 45x + -16x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2

Combine like terms: 23 + 35 = 58
58 + 45x + -16x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2

Combine like terms: 45x + -16x = 29x
58 + 29x + 18x2 + -12x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2

Combine like terms: 18x2 + -12x2 = 6x2
58 + 29x + 6x2 = -35 + 16x + 12x2 + 35 + -16x + -12x2

Reorder the terms:
58 + 29x + 6x2 = -35 + 35 + 16x + -16x + 12x2 + -12x2

Combine like terms: -35 + 35 = 0
58 + 29x + 6x2 = 0 + 16x + -16x + 12x2 + -12x2
58 + 29x + 6x2 = 16x + -16x + 12x2 + -12x2

Combine like terms: 16x + -16x = 0
58 + 29x + 6x2 = 0 + 12x2 + -12x2
58 + 29x + 6x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
58 + 29x + 6x2 = 0

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

Divide each side by '6'.
9.666666667 + 4.833333333x + x2 = 0

Move the constant term to the right:

Add '-9.666666667' to each side of the equation.
9.666666667 + 4.833333333x + -9.666666667 + x2 = 0 + -9.666666667

Reorder the terms:
9.666666667 + -9.666666667 + 4.833333333x + x2 = 0 + -9.666666667

Combine like terms: 9.666666667 + -9.666666667 = 0.000000000
0.000000000 + 4.833333333x + x2 = 0 + -9.666666667
4.833333333x + x2 = 0 + -9.666666667

Combine like terms: 0 + -9.666666667 = -9.666666667
4.833333333x + x2 = -9.666666667

The x term is 4.833333333x.  Take half its coefficient (2.416666667).
Square it (5.840277779) and add it to both sides.

Add '5.840277779' to each side of the equation.
4.833333333x + 5.840277779 + x2 = -9.666666667 + 5.840277779

Reorder the terms:
5.840277779 + 4.833333333x + x2 = -9.666666667 + 5.840277779

Combine like terms: -9.666666667 + 5.840277779 = -3.826388888
5.840277779 + 4.833333333x + x2 = -3.826388888

Factor a perfect square on the left side:
(x + 2.416666667)(x + 2.416666667) = -3.826388888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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