5x(2x-7)-12=5x(6x+3)

Solution for 5x(2x-7)-12=5x(6x+3) equation:

Simplifying
5x(2x + -7) + -12 = 5x(6x + 3)

Reorder the terms:
5x(-7 + 2x) + -12 = 5x(6x + 3)
(-7 * 5x + 2x * 5x) + -12 = 5x(6x + 3)
(-35x + 10x2) + -12 = 5x(6x + 3)

Reorder the terms:
-12 + -35x + 10x2 = 5x(6x + 3)

Reorder the terms:
-12 + -35x + 10x2 = 5x(3 + 6x)
-12 + -35x + 10x2 = (3 * 5x + 6x * 5x)
-12 + -35x + 10x2 = (15x + 30x2)

Solving
-12 + -35x + 10x2 = 15x + 30x2

Solving for variable 'x'.

Reorder the terms:
-12 + -35x + -15x + 10x2 + -30x2 = 15x + 30x2 + -15x + -30x2

Combine like terms: -35x + -15x = -50x
-12 + -50x + 10x2 + -30x2 = 15x + 30x2 + -15x + -30x2

Combine like terms: 10x2 + -30x2 = -20x2
-12 + -50x + -20x2 = 15x + 30x2 + -15x + -30x2

Reorder the terms:
-12 + -50x + -20x2 = 15x + -15x + 30x2 + -30x2

Combine like terms: 15x + -15x = 0
-12 + -50x + -20x2 = 0 + 30x2 + -30x2
-12 + -50x + -20x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
-12 + -50x + -20x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(6 + 25x + 10x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(6 + 25x + 10x2)' equal to zero and attempt to solve:

Simplifying
6 + 25x + 10x2 = 0

Solving
6 + 25x + 10x2 = 0

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

Divide each side by '10'.
0.6 + 2.5x + x2 = 0.0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2.5x + -0.6 + x2 = 0.0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2.5x + x2 = 0.0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2.5x + x2 = 0.0 + -0.6
2.5x + x2 = 0.0 + -0.6

Combine like terms: 0.0 + -0.6 = -0.6
2.5x + x2 = -0.6

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -0.6 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -0.6 + 1.5625

Combine like terms: -0.6 + 1.5625 = 0.9625
1.5625 + 2.5x + x2 = 0.9625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.9625

Calculate the square root of the right side: 0.981070844

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.981070844 and -0.981070844.

Subproblem 1
x + 1.25 = 0.981070844

Simplifying
x + 1.25 = 0.981070844

Reorder the terms:
1.25 + x = 0.981070844

Solving
1.25 + x = 0.981070844

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.981070844 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.981070844 + -1.25
x = 0.981070844 + -1.25

Combine like terms: 0.981070844 + -1.25 = -0.268929156
x = -0.268929156

Simplifying
x = -0.268929156

Subproblem 2
x + 1.25 = -0.981070844

Simplifying
x + 1.25 = -0.981070844

Reorder the terms:
1.25 + x = -0.981070844

Solving
1.25 + x = -0.981070844

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.981070844 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.981070844 + -1.25
x = -0.981070844 + -1.25

Combine like terms: -0.981070844 + -1.25 = -2.231070844
x = -2.231070844

Simplifying
x = -2.231070844

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.268929156, -2.231070844}
Solution
x = {-0.268929156, -2.231070844}