7(2x^2-9x)+5x(9-2x+3x^2)=0

Solution for 7(2x^2-9x)+5x(9-2x+3x^2)=0 equation:

Simplifying
7(2x2 + -9x) + 5x(9 + -2x + 3x2) = 0

Reorder the terms:
7(-9x + 2x2) + 5x(9 + -2x + 3x2) = 0
(-9x * 7 + 2x2 * 7) + 5x(9 + -2x + 3x2) = 0
(-63x + 14x2) + 5x(9 + -2x + 3x2) = 0
-63x + 14x2 + (9 * 5x + -2x * 5x + 3x2 * 5x) = 0
-63x + 14x2 + (45x + -10x2 + 15x3) = 0

Reorder the terms:
-63x + 45x + 14x2 + -10x2 + 15x3 = 0

Combine like terms: -63x + 45x = -18x
-18x + 14x2 + -10x2 + 15x3 = 0

Combine like terms: 14x2 + -10x2 = 4x2
-18x + 4x2 + 15x3 = 0

Solving
-18x + 4x2 + 15x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-18 + 4x + 15x2) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-18 + 4x + 15x2)' equal to zero and attempt to solve:

Simplifying
-18 + 4x + 15x2 = 0

Solving
-18 + 4x + 15x2 = 0

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

Divide each side by '15'.
-1.2 + 0.2666666667x + x2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 0.2666666667x + 1.2 + x2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 0.2666666667x + x2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 0.2666666667x + x2 = 0 + 1.2
0.2666666667x + x2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
0.2666666667x + x2 = 1.2

The x term is 0.2666666667x.  Take half its coefficient (0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
0.2666666667x + 0.01777777780 + x2 = 1.2 + 0.01777777780

Reorder the terms:
0.01777777780 + 0.2666666667x + x2 = 1.2 + 0.01777777780

Combine like terms: 1.2 + 0.01777777780 = 1.2177777778
0.01777777780 + 0.2666666667x + x2 = 1.2177777778

Factor a perfect square on the left side:
(x + 0.1333333334)(x + 0.1333333334) = 1.2177777778

Calculate the square root of the right side: 1.10352969

Break this problem into two subproblems by setting 
(x + 0.1333333334) equal to 1.10352969 and -1.10352969.

Subproblem 1
x + 0.1333333334 = 1.10352969

Simplifying
x + 0.1333333334 = 1.10352969

Reorder the terms:
0.1333333334 + x = 1.10352969

Solving
0.1333333334 + x = 1.10352969

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = 1.10352969 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = 1.10352969 + -0.1333333334
x = 1.10352969 + -0.1333333334

Combine like terms: 1.10352969 + -0.1333333334 = 0.9701963566
x = 0.9701963566

Simplifying
x = 0.9701963566

Subproblem 2
x + 0.1333333334 = -1.10352969

Simplifying
x + 0.1333333334 = -1.10352969

Reorder the terms:
0.1333333334 + x = -1.10352969

Solving
0.1333333334 + x = -1.10352969

Solving for variable 'x'.

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

Add '-0.1333333334' to each side of the equation.
0.1333333334 + -0.1333333334 + x = -1.10352969 + -0.1333333334

Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000
0.0000000000 + x = -1.10352969 + -0.1333333334
x = -1.10352969 + -0.1333333334

Combine like terms: -1.10352969 + -0.1333333334 = -1.2368630234
x = -1.2368630234

Simplifying
x = -1.2368630234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9701963566, -1.2368630234}
Solution
x = {0, 0.9701963566, -1.2368630234}