3x(2x-15)=90

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Solution for 3x(2x-15)=90 equation: 


Simplifying
3x(2x + -15) = 90

Reorder the terms:
3x(-15 + 2x) = 90
(-15 * 3x + 2x * 3x) = 90
(-45x + 6x2) = 90

Solving
-45x + 6x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + -45x + 6x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -45x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + -15x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-30 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
-30 + -15x + 2x2 = 0

Solving
-30 + -15x + 2x2 = 0

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

Divide each side by '2'.
-15 + -7.5x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -7.5x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -7.5x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -7.5x + x2 = 0 + 15
-7.5x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-7.5x + x2 = 15

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 15 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 15 + 14.0625

Combine like terms: 15 + 14.0625 = 29.0625
14.0625 + -7.5x + x2 = 29.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 29.0625

Calculate the square root of the right side: 5.390964663

Break this problem into two subproblems by setting 
(x + -3.75) equal to 5.390964663 and -5.390964663.


Subproblem 1
x + -3.75 = 5.390964663

Simplifying
x + -3.75 = 5.390964663

Reorder the terms:
-3.75 + x = 5.390964663

Solving
-3.75 + x = 5.390964663

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 5.390964663 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 5.390964663 + 3.75
x = 5.390964663 + 3.75

Combine like terms: 5.390964663 + 3.75 = 9.140964663
x = 9.140964663

Simplifying
x = 9.140964663


Subproblem 2
x + -3.75 = -5.390964663

Simplifying
x + -3.75 = -5.390964663

Reorder the terms:
-3.75 + x = -5.390964663

Solving
-3.75 + x = -5.390964663

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -5.390964663 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -5.390964663 + 3.75
x = -5.390964663 + 3.75

Combine like terms: -5.390964663 + 3.75 = -1.640964663
x = -1.640964663

Simplifying
x = -1.640964663


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.140964663, -1.640964663}
Solution
x = {9.140964663, -1.640964663}

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