4(1-3n)-14=4(2n+3)19n

Solution for 4(1-3n)-14=4(2n+3)19n equation:

Simplifying
4(1 + -3n) + -14 = 4(2n + 3) * 19n
(1 * 4 + -3n * 4) + -14 = 4(2n + 3) * 19n
(4 + -12n) + -14 = 4(2n + 3) * 19n

Reorder the terms:
4 + -14 + -12n = 4(2n + 3) * 19n

Combine like terms: 4 + -14 = -10
-10 + -12n = 4(2n + 3) * 19n

Reorder the terms:
-10 + -12n = 4(3 + 2n) * 19n

Reorder the terms for easier multiplication:
-10 + -12n = 4 * 19n(3 + 2n)

Multiply 4 * 19
-10 + -12n = 76n(3 + 2n)
-10 + -12n = (3 * 76n + 2n * 76n)
-10 + -12n = (228n + 152n2)

Solving
-10 + -12n = 228n + 152n2

Solving for variable 'n'.

Combine like terms: -12n + -228n = -240n
-10 + -240n + -152n2 = 228n + 152n2 + -228n + -152n2

Reorder the terms:
-10 + -240n + -152n2 = 228n + -228n + 152n2 + -152n2

Combine like terms: 228n + -228n = 0
-10 + -240n + -152n2 = 0 + 152n2 + -152n2
-10 + -240n + -152n2 = 152n2 + -152n2

Combine like terms: 152n2 + -152n2 = 0
-10 + -240n + -152n2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 120n + 76n2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(5 + 120n + 76n2)' equal to zero and attempt to solve:

Simplifying
5 + 120n + 76n2 = 0

Solving
5 + 120n + 76n2 = 0

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

Divide each side by '76'.
0.06578947368 + 1.578947368n + n2 = 0

Move the constant term to the right:

Add '-0.06578947368' to each side of the equation.
0.06578947368 + 1.578947368n + -0.06578947368 + n2 = 0 + -0.06578947368

Reorder the terms:
0.06578947368 + -0.06578947368 + 1.578947368n + n2 = 0 + -0.06578947368

Combine like terms: 0.06578947368 + -0.06578947368 = 0.00000000000
0.00000000000 + 1.578947368n + n2 = 0 + -0.06578947368
1.578947368n + n2 = 0 + -0.06578947368

Combine like terms: 0 + -0.06578947368 = -0.06578947368
1.578947368n + n2 = -0.06578947368

The n term is 1.578947368n.  Take half its coefficient (0.789473684).
Square it (0.6232686977) and add it to both sides.

Add '0.6232686977' to each side of the equation.
1.578947368n + 0.6232686977 + n2 = -0.06578947368 + 0.6232686977

Reorder the terms:
0.6232686977 + 1.578947368n + n2 = -0.06578947368 + 0.6232686977

Combine like terms: -0.06578947368 + 0.6232686977 = 0.55747922402
0.6232686977 + 1.578947368n + n2 = 0.55747922402

Factor a perfect square on the left side:
(n + 0.789473684)(n + 0.789473684) = 0.55747922402

Calculate the square root of the right side: 0.746645313

Break this problem into two subproblems by setting 
(n + 0.789473684) equal to 0.746645313 and -0.746645313.

Subproblem 1
n + 0.789473684 = 0.746645313

Simplifying
n + 0.789473684 = 0.746645313

Reorder the terms:
0.789473684 + n = 0.746645313

Solving
0.789473684 + n = 0.746645313

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.789473684' to each side of the equation.
0.789473684 + -0.789473684 + n = 0.746645313 + -0.789473684

Combine like terms: 0.789473684 + -0.789473684 = 0.000000000
0.000000000 + n = 0.746645313 + -0.789473684
n = 0.746645313 + -0.789473684

Combine like terms: 0.746645313 + -0.789473684 = -0.042828371
n = -0.042828371

Simplifying
n = -0.042828371

Subproblem 2
n + 0.789473684 = -0.746645313

Simplifying
n + 0.789473684 = -0.746645313

Reorder the terms:
0.789473684 + n = -0.746645313

Solving
0.789473684 + n = -0.746645313

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.789473684' to each side of the equation.
0.789473684 + -0.789473684 + n = -0.746645313 + -0.789473684

Combine like terms: 0.789473684 + -0.789473684 = 0.000000000
0.000000000 + n = -0.746645313 + -0.789473684
n = -0.746645313 + -0.789473684

Combine like terms: -0.746645313 + -0.789473684 = -1.536118997
n = -1.536118997

Simplifying
n = -1.536118997

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.042828371, -1.536118997}
Solution
n = {-0.042828371, -1.536118997}