-5n(2n-3)=7(3-n)

Solution for -5n(2n-3)=7(3-n) equation:

Simplifying
-5n(2n + -3) = 7(3 + -1n)

Reorder the terms:
-5n(-3 + 2n) = 7(3 + -1n)
(-3 * -5n + 2n * -5n) = 7(3 + -1n)
(15n + -10n2) = 7(3 + -1n)
15n + -10n2 = (3 * 7 + -1n * 7)
15n + -10n2 = (21 + -7n)

Solving
15n + -10n2 = 21 + -7n

Solving for variable 'n'.

Reorder the terms:
-21 + 15n + 7n + -10n2 = 21 + -7n + -21 + 7n

Combine like terms: 15n + 7n = 22n
-21 + 22n + -10n2 = 21 + -7n + -21 + 7n

Reorder the terms:
-21 + 22n + -10n2 = 21 + -21 + -7n + 7n

Combine like terms: 21 + -21 = 0
-21 + 22n + -10n2 = 0 + -7n + 7n
-21 + 22n + -10n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-21 + 22n + -10n2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
2.1 + -2.2n + n2 = 0.0

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + -2.2n + -2.1 + n2 = 0.0 + -2.1

Reorder the terms:
2.1 + -2.1 + -2.2n + n2 = 0.0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + -2.2n + n2 = 0.0 + -2.1
-2.2n + n2 = 0.0 + -2.1

Combine like terms: 0.0 + -2.1 = -2.1
-2.2n + n2 = -2.1

The n term is -2.2n.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2n + 1.21 + n2 = -2.1 + 1.21

Reorder the terms:
1.21 + -2.2n + n2 = -2.1 + 1.21

Combine like terms: -2.1 + 1.21 = -0.89
1.21 + -2.2n + n2 = -0.89

Factor a perfect square on the left side:
(n + -1.1)(n + -1.1) = -0.89

Can't calculate square root of the right side.

The solution to this equation could not be determined.