7(12x*3)7x=36+56x

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Solution for 7(12x*3)7x=36+56x equation:


Simplifying
7(12x * 3) * 7x = 36 + 56x

Reorder the terms for easier multiplication:
7(12 * 3x) * 7x = 36 + 56x

Multiply 12 * 3
7(36x) * 7x = 36 + 56x

Remove parenthesis around (36x)
7 * 36x * 7x = 36 + 56x

Reorder the terms for easier multiplication:
7 * 36 * 7x * x = 36 + 56x

Multiply 7 * 36
252 * 7x * x = 36 + 56x

Multiply 252 * 7
1764x * x = 36 + 56x

Multiply x * x
1764x2 = 36 + 56x

Solving
1764x2 = 36 + 56x

Solving for variable 'x'.

Reorder the terms:
-36 + -56x + 1764x2 = 36 + 56x + -36 + -56x

Reorder the terms:
-36 + -56x + 1764x2 = 36 + -36 + 56x + -56x

Combine like terms: 36 + -36 = 0
-36 + -56x + 1764x2 = 0 + 56x + -56x
-36 + -56x + 1764x2 = 56x + -56x

Combine like terms: 56x + -56x = 0
-36 + -56x + 1764x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -14x + 441x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-9 + -14x + 441x2)' equal to zero and attempt to solve:

Simplifying
-9 + -14x + 441x2 = 0

Solving
-9 + -14x + 441x2 = 0

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

Divide each side by '441'.
-0.02040816327 + -0.03174603175x + x2 = 0

Move the constant term to the right:

Add '0.02040816327' to each side of the equation.
-0.02040816327 + -0.03174603175x + 0.02040816327 + x2 = 0 + 0.02040816327

Reorder the terms:
-0.02040816327 + 0.02040816327 + -0.03174603175x + x2 = 0 + 0.02040816327

Combine like terms: -0.02040816327 + 0.02040816327 = 0.00000000000
0.00000000000 + -0.03174603175x + x2 = 0 + 0.02040816327
-0.03174603175x + x2 = 0 + 0.02040816327

Combine like terms: 0 + 0.02040816327 = 0.02040816327
-0.03174603175x + x2 = 0.02040816327

The x term is -0.03174603175x.  Take half its coefficient (-0.01587301588).
Square it (0.0002519526331) and add it to both sides.

Add '0.0002519526331' to each side of the equation.
-0.03174603175x + 0.0002519526331 + x2 = 0.02040816327 + 0.0002519526331

Reorder the terms:
0.0002519526331 + -0.03174603175x + x2 = 0.02040816327 + 0.0002519526331

Combine like terms: 0.02040816327 + 0.0002519526331 = 0.0206601159031
0.0002519526331 + -0.03174603175x + x2 = 0.0206601159031

Factor a perfect square on the left side:
(x + -0.01587301588)(x + -0.01587301588) = 0.0206601159031

Calculate the square root of the right side: 0.143736272

Break this problem into two subproblems by setting 
(x + -0.01587301588) equal to 0.143736272 and -0.143736272.


Subproblem 1
x + -0.01587301588 = 0.143736272

Simplifying
x + -0.01587301588 = 0.143736272

Reorder the terms:
-0.01587301588 + x = 0.143736272

Solving
-0.01587301588 + x = 0.143736272

Solving for variable 'x'.

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

Add '0.01587301588' to each side of the equation.
-0.01587301588 + 0.01587301588 + x = 0.143736272 + 0.01587301588

Combine like terms: -0.01587301588 + 0.01587301588 = 0.00000000000
0.00000000000 + x = 0.143736272 + 0.01587301588
x = 0.143736272 + 0.01587301588

Combine like terms: 0.143736272 + 0.01587301588 = 0.15960928788
x = 0.15960928788

Simplifying
x = 0.15960928788


Subproblem 2
x + -0.01587301588 = -0.143736272

Simplifying
x + -0.01587301588 = -0.143736272

Reorder the terms:
-0.01587301588 + x = -0.143736272

Solving
-0.01587301588 + x = -0.143736272

Solving for variable 'x'.

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

Add '0.01587301588' to each side of the equation.
-0.01587301588 + 0.01587301588 + x = -0.143736272 + 0.01587301588

Combine like terms: -0.01587301588 + 0.01587301588 = 0.00000000000
0.00000000000 + x = -0.143736272 + 0.01587301588
x = -0.143736272 + 0.01587301588

Combine like terms: -0.143736272 + 0.01587301588 = -0.12786325612
x = -0.12786325612

Simplifying
x = -0.12786325612


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.15960928788, -0.12786325612}
Solution
x = {0.15960928788, -0.12786325612}

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