(3x+12)(5x-10)=30

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Solution for (3x+12)(5x-10)=30 equation: 


Simplifying
(3x + 12)(5x + -10) = 30

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

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

Multiply (12 + 3x) * (-10 + 5x)
(12(-10 + 5x) + 3x * (-10 + 5x)) = 30
((-10 * 12 + 5x * 12) + 3x * (-10 + 5x)) = 30
((-120 + 60x) + 3x * (-10 + 5x)) = 30
(-120 + 60x + (-10 * 3x + 5x * 3x)) = 30
(-120 + 60x + (-30x + 15x2)) = 30

Combine like terms: 60x + -30x = 30x
(-120 + 30x + 15x2) = 30

Solving
-120 + 30x + 15x2 = 30

Solving for variable 'x'.

Reorder the terms:
-120 + -30 + 30x + 15x2 = 30 + -30

Combine like terms: -120 + -30 = -150
-150 + 30x + 15x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-150 + 30x + 15x2 = 0

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

Ignore the factor 15.

Subproblem 1
Set the factor '(-10 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + 2x + x2 = 0

Solving
-10 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 2x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 2x + x2 = 0 + 10
2x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
2x + x2 = 10

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 10 + 1

Reorder the terms:
1 + 2x + x2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + 2x + x2 = 11

Factor a perfect square on the left side:
(x + 1)(x + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 1) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 1 = 3.31662479

Simplifying
x + 1 = 3.31662479

Reorder the terms:
1 + x = 3.31662479

Solving
1 + x = 3.31662479

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.31662479 + -1
x = 3.31662479 + -1

Combine like terms: 3.31662479 + -1 = 2.31662479
x = 2.31662479

Simplifying
x = 2.31662479


Subproblem 2
x + 1 = -3.31662479

Simplifying
x + 1 = -3.31662479

Reorder the terms:
1 + x = -3.31662479

Solving
1 + x = -3.31662479

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.31662479 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.31662479 + -1
x = -3.31662479 + -1

Combine like terms: -3.31662479 + -1 = -4.31662479
x = -4.31662479

Simplifying
x = -4.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.31662479, -4.31662479}
Solution
x = {2.31662479, -4.31662479}

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