10x+12=4x(x+6)

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Solution for 10x+12=4x(x+6) equation: 


Simplifying
10x + 12 = 4x(x + 6)

Reorder the terms:
12 + 10x = 4x(x + 6)

Reorder the terms:
12 + 10x = 4x(6 + x)
12 + 10x = (6 * 4x + x * 4x)
12 + 10x = (24x + 4x2)

Solving
12 + 10x = 24x + 4x2

Solving for variable 'x'.

Combine like terms: 10x + -24x = -14x
12 + -14x + -4x2 = 24x + 4x2 + -24x + -4x2

Reorder the terms:
12 + -14x + -4x2 = 24x + -24x + 4x2 + -4x2

Combine like terms: 24x + -24x = 0
12 + -14x + -4x2 = 0 + 4x2 + -4x2
12 + -14x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
12 + -14x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -7x + -2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -7x + -2x2)' equal to zero and attempt to solve:

Simplifying
6 + -7x + -2x2 = 0

Solving
6 + -7x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + 3.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 3.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 3.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 3.5x + x2 = 0 + 3
3.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
3.5x + x2 = 3

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 3 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 3 + 3.0625

Combine like terms: 3 + 3.0625 = 6.0625
3.0625 + 3.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + 1.75 = 2.46221445

Simplifying
x + 1.75 = 2.46221445

Reorder the terms:
1.75 + x = 2.46221445

Solving
1.75 + x = 2.46221445

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.46221445 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.46221445 + -1.75
x = 2.46221445 + -1.75

Combine like terms: 2.46221445 + -1.75 = 0.71221445
x = 0.71221445

Simplifying
x = 0.71221445


Subproblem 2
x + 1.75 = -2.46221445

Simplifying
x + 1.75 = -2.46221445

Reorder the terms:
1.75 + x = -2.46221445

Solving
1.75 + x = -2.46221445

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.46221445 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.46221445 + -1.75
x = -2.46221445 + -1.75

Combine like terms: -2.46221445 + -1.75 = -4.21221445
x = -4.21221445

Simplifying
x = -4.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.71221445, -4.21221445}
Solution
x = {0.71221445, -4.21221445}

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