2x(15x+12)=5x+42-x

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Solution for 2x(15x+12)=5x+42-x equation:


Simplifying
2x(15x + 12) = 5x + 42 + -1x

Reorder the terms:
2x(12 + 15x) = 5x + 42 + -1x
(12 * 2x + 15x * 2x) = 5x + 42 + -1x
(24x + 30x2) = 5x + 42 + -1x

Reorder the terms:
24x + 30x2 = 42 + 5x + -1x

Combine like terms: 5x + -1x = 4x
24x + 30x2 = 42 + 4x

Solving
24x + 30x2 = 42 + 4x

Solving for variable 'x'.

Reorder the terms:
-42 + 24x + -4x + 30x2 = 42 + 4x + -42 + -4x

Combine like terms: 24x + -4x = 20x
-42 + 20x + 30x2 = 42 + 4x + -42 + -4x

Reorder the terms:
-42 + 20x + 30x2 = 42 + -42 + 4x + -4x

Combine like terms: 42 + -42 = 0
-42 + 20x + 30x2 = 0 + 4x + -4x
-42 + 20x + 30x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-42 + 20x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 10x + 15x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-21 + 10x + 15x2)' equal to zero and attempt to solve:

Simplifying
-21 + 10x + 15x2 = 0

Solving
-21 + 10x + 15x2 = 0

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

Divide each side by '15'.
-1.4 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 0.6666666667x + 1.4 + x2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 0.6666666667x + x2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 0.6666666667x + x2 = 0 + 1.4
0.6666666667x + x2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
0.6666666667x + x2 = 1.4

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1.4 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1.4 + 0.1111111112

Combine like terms: 1.4 + 0.1111111112 = 1.5111111112
0.1111111112 + 0.6666666667x + x2 = 1.5111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.5111111112

Calculate the square root of the right side: 1.229272594

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.229272594 and -1.229272594.


Subproblem 1
x + 0.3333333334 = 1.229272594

Simplifying
x + 0.3333333334 = 1.229272594

Reorder the terms:
0.3333333334 + x = 1.229272594

Solving
0.3333333334 + x = 1.229272594

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.229272594 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.229272594 + -0.3333333334
x = 1.229272594 + -0.3333333334

Combine like terms: 1.229272594 + -0.3333333334 = 0.8959392606
x = 0.8959392606

Simplifying
x = 0.8959392606


Subproblem 2
x + 0.3333333334 = -1.229272594

Simplifying
x + 0.3333333334 = -1.229272594

Reorder the terms:
0.3333333334 + x = -1.229272594

Solving
0.3333333334 + x = -1.229272594

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.229272594 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.229272594 + -0.3333333334
x = -1.229272594 + -0.3333333334

Combine like terms: -1.229272594 + -0.3333333334 = -1.5626059274
x = -1.5626059274

Simplifying
x = -1.5626059274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8959392606, -1.5626059274}
Solution
x = {0.8959392606, -1.5626059274}

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