3x(8x+2)=90

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Solution for 3x(8x+2)=90 equation: 


Simplifying
3x(8x + 2) = 90

Reorder the terms:
3x(2 + 8x) = 90
(2 * 3x + 8x * 3x) = 90
(6x + 24x2) = 90

Solving
6x + 24x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 6x + 24x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 6x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + x + 4x2) = 0

Ignore the factor 6.

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

Simplifying
-15 + x + 4x2 = 0

Solving
-15 + x + 4x2 = 0

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

Divide each side by '4'.
-3.75 + 0.25x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + 0.25x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + 0.25x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + 0.25x + x2 = 0 + 3.75
0.25x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
0.25x + x2 = 3.75

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25x + 0.25 + x2 = 3.75 + 0.25

Reorder the terms:
0.25 + 0.25x + x2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
0.25 + 0.25x + x2 = 4

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2 and -2.


Subproblem 1
x + 0.5 = 2

Simplifying
x + 0.5 = 2

Reorder the terms:
0.5 + x = 2

Solving
0.5 + x = 2

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2 + -0.5
x = 2 + -0.5

Combine like terms: 2 + -0.5 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + 0.5 = -2

Simplifying
x + 0.5 = -2

Reorder the terms:
0.5 + x = -2

Solving
0.5 + x = -2

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2 + -0.5
x = -2 + -0.5

Combine like terms: -2 + -0.5 = -2.5
x = -2.5

Simplifying
x = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -2.5}
Solution
x = {1.5, -2.5}

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