6x[5x-7]=432

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Solution for 6x[5x-7]=432 equation: 


Simplifying
6x[5x + -7] = 432

Reorder the terms:
6x[-7 + 5x] = 432
[-7 * 6x + 5x * 6x] = 432
[-42x + 30x2] = 432

Solving
-42x + 30x2 = 432

Solving for variable 'x'.

Reorder the terms:
-432 + -42x + 30x2 = 432 + -432

Combine like terms: 432 + -432 = 0
-432 + -42x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-72 + -7x + 5x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-72 + -7x + 5x2)' equal to zero and attempt to solve:

Simplifying
-72 + -7x + 5x2 = 0

Solving
-72 + -7x + 5x2 = 0

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

Divide each side by '5'.
-14.4 + -1.4x + x2 = 0

Move the constant term to the right:

Add '14.4' to each side of the equation.
-14.4 + -1.4x + 14.4 + x2 = 0 + 14.4

Reorder the terms:
-14.4 + 14.4 + -1.4x + x2 = 0 + 14.4

Combine like terms: -14.4 + 14.4 = 0.0
0.0 + -1.4x + x2 = 0 + 14.4
-1.4x + x2 = 0 + 14.4

Combine like terms: 0 + 14.4 = 14.4
-1.4x + x2 = 14.4

The x term is -1.4x.  Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 14.4 + 0.49

Reorder the terms:
0.49 + -1.4x + x2 = 14.4 + 0.49

Combine like terms: 14.4 + 0.49 = 14.89
0.49 + -1.4x + x2 = 14.89

Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 14.89

Calculate the square root of the right side: 3.858756276

Break this problem into two subproblems by setting 
(x + -0.7) equal to 3.858756276 and -3.858756276.


Subproblem 1
x + -0.7 = 3.858756276

Simplifying
x + -0.7 = 3.858756276

Reorder the terms:
-0.7 + x = 3.858756276

Solving
-0.7 + x = 3.858756276

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 3.858756276 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 3.858756276 + 0.7
x = 3.858756276 + 0.7

Combine like terms: 3.858756276 + 0.7 = 4.558756276
x = 4.558756276

Simplifying
x = 4.558756276


Subproblem 2
x + -0.7 = -3.858756276

Simplifying
x + -0.7 = -3.858756276

Reorder the terms:
-0.7 + x = -3.858756276

Solving
-0.7 + x = -3.858756276

Solving for variable 'x'.

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

Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -3.858756276 + 0.7

Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -3.858756276 + 0.7
x = -3.858756276 + 0.7

Combine like terms: -3.858756276 + 0.7 = -3.158756276
x = -3.158756276

Simplifying
x = -3.158756276


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.558756276, -3.158756276}
Solution
x = {4.558756276, -3.158756276}

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