4(2x-5)+15=3x(x+10)

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Solution for 4(2x-5)+15=3x(x+10) equation: 


Simplifying
4(2x + -5) + 15 = 3x(x + 10)

Reorder the terms:
4(-5 + 2x) + 15 = 3x(x + 10)
(-5 * 4 + 2x * 4) + 15 = 3x(x + 10)
(-20 + 8x) + 15 = 3x(x + 10)

Reorder the terms:
-20 + 15 + 8x = 3x(x + 10)

Combine like terms: -20 + 15 = -5
-5 + 8x = 3x(x + 10)

Reorder the terms:
-5 + 8x = 3x(10 + x)
-5 + 8x = (10 * 3x + x * 3x)
-5 + 8x = (30x + 3x2)

Solving
-5 + 8x = 30x + 3x2

Solving for variable 'x'.

Combine like terms: 8x + -30x = -22x
-5 + -22x + -3x2 = 30x + 3x2 + -30x + -3x2

Reorder the terms:
-5 + -22x + -3x2 = 30x + -30x + 3x2 + -3x2

Combine like terms: 30x + -30x = 0
-5 + -22x + -3x2 = 0 + 3x2 + -3x2
-5 + -22x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + -22x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 22x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 22x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 22x + 3x2 = 0

Solving
5 + 22x + 3x2 = 0

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

Divide each side by '3'.
1.666666667 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 7.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 7.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 7.333333333x + x2 = 0 + -1.666666667
7.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
7.333333333x + x2 = -1.666666667

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = -1.666666667 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = -1.666666667 + 13.44444445

Combine like terms: -1.666666667 + 13.44444445 = 11.777777783
13.44444445 + 7.333333333x + x2 = 11.777777783

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 11.777777783

Calculate the square root of the right side: 3.431876714

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 3.431876714 and -3.431876714.


Subproblem 1
x + 3.666666667 = 3.431876714

Simplifying
x + 3.666666667 = 3.431876714

Reorder the terms:
3.666666667 + x = 3.431876714

Solving
3.666666667 + x = 3.431876714

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 3.431876714 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 3.431876714 + -3.666666667
x = 3.431876714 + -3.666666667

Combine like terms: 3.431876714 + -3.666666667 = -0.234789953
x = -0.234789953

Simplifying
x = -0.234789953


Subproblem 2
x + 3.666666667 = -3.431876714

Simplifying
x + 3.666666667 = -3.431876714

Reorder the terms:
3.666666667 + x = -3.431876714

Solving
3.666666667 + x = -3.431876714

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -3.431876714 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -3.431876714 + -3.666666667
x = -3.431876714 + -3.666666667

Combine like terms: -3.431876714 + -3.666666667 = -7.098543381
x = -7.098543381

Simplifying
x = -7.098543381


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.234789953, -7.098543381}
Solution
x = {-0.234789953, -7.098543381}

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