5x(x-3)+69=15x(7-5x)

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Solution for 5x(x-3)+69=15x(7-5x) equation: 


Simplifying
5x(x + -3) + 69 = 15x(7 + -5x)

Reorder the terms:
5x(-3 + x) + 69 = 15x(7 + -5x)
(-3 * 5x + x * 5x) + 69 = 15x(7 + -5x)
(-15x + 5x2) + 69 = 15x(7 + -5x)

Reorder the terms:
69 + -15x + 5x2 = 15x(7 + -5x)
69 + -15x + 5x2 = (7 * 15x + -5x * 15x)
69 + -15x + 5x2 = (105x + -75x2)

Solving
69 + -15x + 5x2 = 105x + -75x2

Solving for variable 'x'.

Reorder the terms:
69 + -15x + -105x + 5x2 + 75x2 = 105x + -75x2 + -105x + 75x2

Combine like terms: -15x + -105x = -120x
69 + -120x + 5x2 + 75x2 = 105x + -75x2 + -105x + 75x2

Combine like terms: 5x2 + 75x2 = 80x2
69 + -120x + 80x2 = 105x + -75x2 + -105x + 75x2

Reorder the terms:
69 + -120x + 80x2 = 105x + -105x + -75x2 + 75x2

Combine like terms: 105x + -105x = 0
69 + -120x + 80x2 = 0 + -75x2 + 75x2
69 + -120x + 80x2 = -75x2 + 75x2

Combine like terms: -75x2 + 75x2 = 0
69 + -120x + 80x2 = 0

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

Divide each side by '80'.
0.8625 + -1.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.8625' to each side of the equation.
0.8625 + -1.5x + -0.8625 + x2 = 0.0 + -0.8625

Reorder the terms:
0.8625 + -0.8625 + -1.5x + x2 = 0.0 + -0.8625

Combine like terms: 0.8625 + -0.8625 = 0.0000
0.0000 + -1.5x + x2 = 0.0 + -0.8625
-1.5x + x2 = 0.0 + -0.8625

Combine like terms: 0.0 + -0.8625 = -0.8625
-1.5x + x2 = -0.8625

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.8625 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.8625 + 0.5625

Combine like terms: -0.8625 + 0.5625 = -0.3
0.5625 + -1.5x + x2 = -0.3

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = -0.3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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