3x(5x-6)+5(9x-4)=

Solution for 3x(5x-6)+5(9x-4)= equation:

Simplifying
3x(5x + -6) + 5(9x + -4) = 0

Reorder the terms:
3x(-6 + 5x) + 5(9x + -4) = 0
(-6 * 3x + 5x * 3x) + 5(9x + -4) = 0
(-18x + 15x2) + 5(9x + -4) = 0

Reorder the terms:
-18x + 15x2 + 5(-4 + 9x) = 0
-18x + 15x2 + (-4 * 5 + 9x * 5) = 0
-18x + 15x2 + (-20 + 45x) = 0

Reorder the terms:
-20 + -18x + 45x + 15x2 = 0

Combine like terms: -18x + 45x = 27x
-20 + 27x + 15x2 = 0

Solving
-20 + 27x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-1.333333333 + 1.8x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.8x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.8x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.8x + x2 = 0 + 1.333333333
1.8x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.8x + x2 = 1.333333333

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 1.333333333 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 1.333333333 + 0.81

Combine like terms: 1.333333333 + 0.81 = 2.143333333
0.81 + 1.8x + x2 = 2.143333333

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 2.143333333

Calculate the square root of the right side: 1.46401275

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.46401275 and -1.46401275.

Subproblem 1
x + 0.9 = 1.46401275

Simplifying
x + 0.9 = 1.46401275

Reorder the terms:
0.9 + x = 1.46401275

Solving
0.9 + x = 1.46401275

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = 1.46401275 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = 1.46401275 + -0.9
x = 1.46401275 + -0.9

Combine like terms: 1.46401275 + -0.9 = 0.56401275
x = 0.56401275

Simplifying
x = 0.56401275

Subproblem 2
x + 0.9 = -1.46401275

Simplifying
x + 0.9 = -1.46401275

Reorder the terms:
0.9 + x = -1.46401275

Solving
0.9 + x = -1.46401275

Solving for variable 'x'.

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

Add '-0.9' to each side of the equation.
0.9 + -0.9 + x = -1.46401275 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + x = -1.46401275 + -0.9
x = -1.46401275 + -0.9

Combine like terms: -1.46401275 + -0.9 = -2.36401275
x = -2.36401275

Simplifying
x = -2.36401275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.56401275, -2.36401275}