4(3x+7)=5x(4x-12)

Solution for 4(3x+7)=5x(4x-12) equation:

Simplifying
4(3x + 7) = 5x(4x + -12)

Reorder the terms:
4(7 + 3x) = 5x(4x + -12)
(7 * 4 + 3x * 4) = 5x(4x + -12)
(28 + 12x) = 5x(4x + -12)

Reorder the terms:
28 + 12x = 5x(-12 + 4x)
28 + 12x = (-12 * 5x + 4x * 5x)
28 + 12x = (-60x + 20x2)

Solving
28 + 12x = -60x + 20x2

Solving for variable 'x'.

Combine like terms: 12x + 60x = 72x
28 + 72x + -20x2 = -60x + 20x2 + 60x + -20x2

Reorder the terms:
28 + 72x + -20x2 = -60x + 60x + 20x2 + -20x2

Combine like terms: -60x + 60x = 0
28 + 72x + -20x2 = 0 + 20x2 + -20x2
28 + 72x + -20x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
28 + 72x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 18x + -5x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(7 + 18x + -5x2)' equal to zero and attempt to solve:

Simplifying
7 + 18x + -5x2 = 0

Solving
7 + 18x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.4 + -3.6x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -3.6x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -3.6x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -3.6x + x2 = 0 + 1.4
-3.6x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-3.6x + x2 = 1.4

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = 1.4 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = 1.4 + 3.24

Combine like terms: 1.4 + 3.24 = 4.64
3.24 + -3.6x + x2 = 4.64

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 4.64

Calculate the square root of the right side: 2.154065923

Break this problem into two subproblems by setting 
(x + -1.8) equal to 2.154065923 and -2.154065923.

Subproblem 1
x + -1.8 = 2.154065923

Simplifying
x + -1.8 = 2.154065923

Reorder the terms:
-1.8 + x = 2.154065923

Solving
-1.8 + x = 2.154065923

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = 2.154065923 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = 2.154065923 + 1.8
x = 2.154065923 + 1.8

Combine like terms: 2.154065923 + 1.8 = 3.954065923
x = 3.954065923

Simplifying
x = 3.954065923

Subproblem 2
x + -1.8 = -2.154065923

Simplifying
x + -1.8 = -2.154065923

Reorder the terms:
-1.8 + x = -2.154065923

Solving
-1.8 + x = -2.154065923

Solving for variable 'x'.

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

Add '1.8' to each side of the equation.
-1.8 + 1.8 + x = -2.154065923 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + x = -2.154065923 + 1.8
x = -2.154065923 + 1.8

Combine like terms: -2.154065923 + 1.8 = -0.354065923
x = -0.354065923

Simplifying
x = -0.354065923

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.954065923, -0.354065923}
Solution
x = {3.954065923, -0.354065923}