9(4x^2+4x+4)=4(x^2-10x+25)

Solution for 9(4x^2+4x+4)=4(x^2-10x+25) equation:

Simplifying
9(4x2 + 4x + 4) = 4(x2 + -10x + 25)

Reorder the terms:
9(4 + 4x + 4x2) = 4(x2 + -10x + 25)
(4 * 9 + 4x * 9 + 4x2 * 9) = 4(x2 + -10x + 25)
(36 + 36x + 36x2) = 4(x2 + -10x + 25)

Reorder the terms:
36 + 36x + 36x2 = 4(25 + -10x + x2)
36 + 36x + 36x2 = (25 * 4 + -10x * 4 + x2 * 4)
36 + 36x + 36x2 = (100 + -40x + 4x2)

Solving
36 + 36x + 36x2 = 100 + -40x + 4x2

Solving for variable 'x'.

Reorder the terms:
36 + -100 + 36x + 40x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 36 + -100 = -64
-64 + 36x + 40x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 36x + 40x = 76x
-64 + 76x + 36x2 + -4x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Combine like terms: 36x2 + -4x2 = 32x2
-64 + 76x + 32x2 = 100 + -40x + 4x2 + -100 + 40x + -4x2

Reorder the terms:
-64 + 76x + 32x2 = 100 + -100 + -40x + 40x + 4x2 + -4x2

Combine like terms: 100 + -100 = 0
-64 + 76x + 32x2 = 0 + -40x + 40x + 4x2 + -4x2
-64 + 76x + 32x2 = -40x + 40x + 4x2 + -4x2

Combine like terms: -40x + 40x = 0
-64 + 76x + 32x2 = 0 + 4x2 + -4x2
-64 + 76x + 32x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-64 + 76x + 32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 19x + 8x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-16 + 19x + 8x2)' equal to zero and attempt to solve:

Simplifying
-16 + 19x + 8x2 = 0

Solving
-16 + 19x + 8x2 = 0

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

Divide each side by '8'.
-2 + 2.375x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2.375x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 2.375x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2.375x + x2 = 0 + 2
2.375x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
2.375x + x2 = 2

The x term is 2.375x.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375x + 1.41015625 + x2 = 2 + 1.41015625

Reorder the terms:
1.41015625 + 2.375x + x2 = 2 + 1.41015625

Combine like terms: 2 + 1.41015625 = 3.41015625
1.41015625 + 2.375x + x2 = 3.41015625

Factor a perfect square on the left side:
(x + 1.1875)(x + 1.1875) = 3.41015625

Calculate the square root of the right side: 1.846660838

Break this problem into two subproblems by setting 
(x + 1.1875) equal to 1.846660838 and -1.846660838.

Subproblem 1
x + 1.1875 = 1.846660838

Simplifying
x + 1.1875 = 1.846660838

Reorder the terms:
1.1875 + x = 1.846660838

Solving
1.1875 + x = 1.846660838

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = 1.846660838 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = 1.846660838 + -1.1875
x = 1.846660838 + -1.1875

Combine like terms: 1.846660838 + -1.1875 = 0.659160838
x = 0.659160838

Simplifying
x = 0.659160838

Subproblem 2
x + 1.1875 = -1.846660838

Simplifying
x + 1.1875 = -1.846660838

Reorder the terms:
1.1875 + x = -1.846660838

Solving
1.1875 + x = -1.846660838

Solving for variable 'x'.

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

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + x = -1.846660838 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + x = -1.846660838 + -1.1875
x = -1.846660838 + -1.1875

Combine like terms: -1.846660838 + -1.1875 = -3.034160838
x = -3.034160838

Simplifying
x = -3.034160838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.659160838, -3.034160838}
Solution
x = {0.659160838, -3.034160838}