3x(5x-10)=3x+12

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Solution for 3x(5x-10)=3x+12 equation: 


Simplifying
3x(5x + -10) = 3x + 12

Reorder the terms:
3x(-10 + 5x) = 3x + 12
(-10 * 3x + 5x * 3x) = 3x + 12
(-30x + 15x2) = 3x + 12

Reorder the terms:
-30x + 15x2 = 12 + 3x

Solving
-30x + 15x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + -30x + -3x + 15x2 = 12 + 3x + -12 + -3x

Combine like terms: -30x + -3x = -33x
-12 + -33x + 15x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + -33x + 15x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + -33x + 15x2 = 0 + 3x + -3x
-12 + -33x + 15x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -33x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -11x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -11x + 5x2)' equal to zero and attempt to solve:

Simplifying
-4 + -11x + 5x2 = 0

Solving
-4 + -11x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + -2.2x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -2.2x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -2.2x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -2.2x + x2 = 0 + 0.8
-2.2x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-2.2x + x2 = 0.8

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 0.8 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 0.8 + 1.21

Combine like terms: 0.8 + 1.21 = 2.01
1.21 + -2.2x + x2 = 2.01

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 2.01

Calculate the square root of the right side: 1.417744688

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.417744688 and -1.417744688.


Subproblem 1
x + -1.1 = 1.417744688

Simplifying
x + -1.1 = 1.417744688

Reorder the terms:
-1.1 + x = 1.417744688

Solving
-1.1 + x = 1.417744688

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 1.417744688 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.417744688 + 1.1
x = 1.417744688 + 1.1

Combine like terms: 1.417744688 + 1.1 = 2.517744688
x = 2.517744688

Simplifying
x = 2.517744688


Subproblem 2
x + -1.1 = -1.417744688

Simplifying
x + -1.1 = -1.417744688

Reorder the terms:
-1.1 + x = -1.417744688

Solving
-1.1 + x = -1.417744688

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -1.417744688 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.417744688 + 1.1
x = -1.417744688 + 1.1

Combine like terms: -1.417744688 + 1.1 = -0.317744688
x = -0.317744688

Simplifying
x = -0.317744688


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.517744688, -0.317744688}
Solution
x = {2.517744688, -0.317744688}

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