4x(2x+9)-2(5x+6)=

Solution for 4x(2x+9)-2(5x+6)= equation:

Simplifying
4x(2x + 9) + -2(5x + 6) = 0

Reorder the terms:
4x(9 + 2x) + -2(5x + 6) = 0
(9 * 4x + 2x * 4x) + -2(5x + 6) = 0
(36x + 8x2) + -2(5x + 6) = 0

Reorder the terms:
36x + 8x2 + -2(6 + 5x) = 0
36x + 8x2 + (6 * -2 + 5x * -2) = 0
36x + 8x2 + (-12 + -10x) = 0

Reorder the terms:
-12 + 36x + -10x + 8x2 = 0

Combine like terms: 36x + -10x = 26x
-12 + 26x + 8x2 = 0

Solving
-12 + 26x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 13x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
-6 + 13x + 4x2 = 0

Solving
-6 + 13x + 4x2 = 0

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

Divide each side by '4'.
-1.5 + 3.25x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3.25x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3.25x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3.25x + x2 = 0 + 1.5
3.25x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3.25x + x2 = 1.5

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = 1.5 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = 1.5 + 2.640625

Combine like terms: 1.5 + 2.640625 = 4.140625
2.640625 + 3.25x + x2 = 4.140625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + 1.625) equal to 2.034852575 and -2.034852575.

Subproblem 1
x + 1.625 = 2.034852575

Simplifying
x + 1.625 = 2.034852575

Reorder the terms:
1.625 + x = 2.034852575

Solving
1.625 + x = 2.034852575

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = 2.034852575 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 2.034852575 + -1.625
x = 2.034852575 + -1.625

Combine like terms: 2.034852575 + -1.625 = 0.409852575
x = 0.409852575

Simplifying
x = 0.409852575

Subproblem 2
x + 1.625 = -2.034852575

Simplifying
x + 1.625 = -2.034852575

Reorder the terms:
1.625 + x = -2.034852575

Solving
1.625 + x = -2.034852575

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = -2.034852575 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -2.034852575 + -1.625
x = -2.034852575 + -1.625

Combine like terms: -2.034852575 + -1.625 = -3.659852575
x = -3.659852575

Simplifying
x = -3.659852575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.409852575, -3.659852575}
Solution
x = {0.409852575, -3.659852575}