4(3x^2-24x+35)=0

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Solution for 4(3x^2-24x+35)=0 equation: 


Simplifying
4(3x2 + -24x + 35) = 0

Reorder the terms:
4(35 + -24x + 3x2) = 0
(35 * 4 + -24x * 4 + 3x2 * 4) = 0
(140 + -96x + 12x2) = 0

Solving
140 + -96x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -24x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(35 + -24x + 3x2)' equal to zero and attempt to solve:

Simplifying
35 + -24x + 3x2 = 0

Solving
35 + -24x + 3x2 = 0

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

Divide each side by '3'.
11.66666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-11.66666667' to each side of the equation.
11.66666667 + -8x + -11.66666667 + x2 = 0 + -11.66666667

Reorder the terms:
11.66666667 + -11.66666667 + -8x + x2 = 0 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + -8x + x2 = 0 + -11.66666667
-8x + x2 = 0 + -11.66666667

Combine like terms: 0 + -11.66666667 = -11.66666667
-8x + x2 = -11.66666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -11.66666667 + 16

Reorder the terms:
16 + -8x + x2 = -11.66666667 + 16

Combine like terms: -11.66666667 + 16 = 4.33333333
16 + -8x + x2 = 4.33333333

Factor a perfect square on the left side:
(x + -4)(x + -4) = 4.33333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + -4) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + -4 = 2.081665999

Simplifying
x + -4 = 2.081665999

Reorder the terms:
-4 + x = 2.081665999

Solving
-4 + x = 2.081665999

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 2.081665999 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.081665999 + 4
x = 2.081665999 + 4

Combine like terms: 2.081665999 + 4 = 6.081665999
x = 6.081665999

Simplifying
x = 6.081665999


Subproblem 2
x + -4 = -2.081665999

Simplifying
x + -4 = -2.081665999

Reorder the terms:
-4 + x = -2.081665999

Solving
-4 + x = -2.081665999

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -2.081665999 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.081665999 + 4
x = -2.081665999 + 4

Combine like terms: -2.081665999 + 4 = 1.918334001
x = 1.918334001

Simplifying
x = 1.918334001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.081665999, 1.918334001}
Solution
x = {6.081665999, 1.918334001}

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