90=3x(4x-15)

Solution for 90=3x(4x-15) equation:

Simplifying
90 = 3x(4x + -15)

Reorder the terms:
90 = 3x(-15 + 4x)
90 = (-15 * 3x + 4x * 3x)
90 = (-45x + 12x2)

Solving
90 = -45x + 12x2

Solving for variable 'x'.

Reorder the terms:
90 + 45x + -12x2 = -45x + 45x + 12x2 + -12x2

Combine like terms: -45x + 45x = 0
90 + 45x + -12x2 = 0 + 12x2 + -12x2
90 + 45x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
90 + 45x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + 15x + -4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(30 + 15x + -4x2)' equal to zero and attempt to solve:

Simplifying
30 + 15x + -4x2 = 0

Solving
30 + 15x + -4x2 = 0

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

Divide each side by '-4'.
-7.5 + -3.75x + x2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3.75x + 7.5 + x2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3.75x + x2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3.75x + x2 = 0 + 7.5
-3.75x + x2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-3.75x + x2 = 7.5

The x term is -3.75x.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75x + 3.515625 + x2 = 7.5 + 3.515625

Reorder the terms:
3.515625 + -3.75x + x2 = 7.5 + 3.515625

Combine like terms: 7.5 + 3.515625 = 11.015625
3.515625 + -3.75x + x2 = 11.015625

Factor a perfect square on the left side:
(x + -1.875)(x + -1.875) = 11.015625

Calculate the square root of the right side: 3.318979512

Break this problem into two subproblems by setting 
(x + -1.875) equal to 3.318979512 and -3.318979512.

Subproblem 1
x + -1.875 = 3.318979512

Simplifying
x + -1.875 = 3.318979512

Reorder the terms:
-1.875 + x = 3.318979512

Solving
-1.875 + x = 3.318979512

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = 3.318979512 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = 3.318979512 + 1.875
x = 3.318979512 + 1.875

Combine like terms: 3.318979512 + 1.875 = 5.193979512
x = 5.193979512

Simplifying
x = 5.193979512

Subproblem 2
x + -1.875 = -3.318979512

Simplifying
x + -1.875 = -3.318979512

Reorder the terms:
-1.875 + x = -3.318979512

Solving
-1.875 + x = -3.318979512

Solving for variable 'x'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + x = -3.318979512 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + x = -3.318979512 + 1.875
x = -3.318979512 + 1.875

Combine like terms: -3.318979512 + 1.875 = -1.443979512
x = -1.443979512

Simplifying
x = -1.443979512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.193979512, -1.443979512}
Solution
x = {5.193979512, -1.443979512}