6x(2x+7)=48

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Solution for 6x(2x+7)=48 equation: 


Simplifying
6x(2x + 7) = 48

Reorder the terms:
6x(7 + 2x) = 48
(7 * 6x + 2x * 6x) = 48
(42x + 12x2) = 48

Solving
42x + 12x2 = 48

Solving for variable 'x'.

Reorder the terms:
-48 + 42x + 12x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + 42x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + 7x + 2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-8 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-8 + 7x + 2x2 = 0

Solving
-8 + 7x + 2x2 = 0

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

Divide each side by '2'.
-4 + 3.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 3.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 3.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3.5x + x2 = 0 + 4
3.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
3.5x + x2 = 4

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 = 4 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 4 + 3.0625

Combine like terms: 4 + 3.0625 = 7.0625
3.0625 + 3.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.657536453 and -2.657536453.


Subproblem 1
x + 1.75 = 2.657536453

Simplifying
x + 1.75 = 2.657536453

Reorder the terms:
1.75 + x = 2.657536453

Solving
1.75 + x = 2.657536453

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 = 2.657536453 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.657536453 + -1.75
x = 2.657536453 + -1.75

Combine like terms: 2.657536453 + -1.75 = 0.907536453
x = 0.907536453

Simplifying
x = 0.907536453


Subproblem 2
x + 1.75 = -2.657536453

Simplifying
x + 1.75 = -2.657536453

Reorder the terms:
1.75 + x = -2.657536453

Solving
1.75 + x = -2.657536453

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 = -2.657536453 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.657536453 + -1.75
x = -2.657536453 + -1.75

Combine like terms: -2.657536453 + -1.75 = -4.407536453
x = -4.407536453

Simplifying
x = -4.407536453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.907536453, -4.407536453}
Solution
x = {0.907536453, -4.407536453}

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