3x(x+4)=30

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Solution for 3x(x+4)=30 equation: 


Simplifying
3x(x + 4) = 30

Reorder the terms:
3x(4 + x) = 30
(4 * 3x + x * 3x) = 30
(12x + 3x2) = 30

Solving
12x + 3x2 = 30

Solving for variable 'x'.

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

Combine like terms: 30 + -30 = 0
-30 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-10 + 4x + x2 = 0

Solving
-10 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 4x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 4x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 4x + x2 = 0 + 10
4x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
4x + x2 = 10

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 10 + 4

Reorder the terms:
4 + 4x + x2 = 10 + 4

Combine like terms: 10 + 4 = 14
4 + 4x + x2 = 14

Factor a perfect square on the left side:
(x + 2)(x + 2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + 2) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + 2 = 3.741657387

Simplifying
x + 2 = 3.741657387

Reorder the terms:
2 + x = 3.741657387

Solving
2 + x = 3.741657387

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.741657387 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.741657387 + -2
x = 3.741657387 + -2

Combine like terms: 3.741657387 + -2 = 1.741657387
x = 1.741657387

Simplifying
x = 1.741657387


Subproblem 2
x + 2 = -3.741657387

Simplifying
x + 2 = -3.741657387

Reorder the terms:
2 + x = -3.741657387

Solving
2 + x = -3.741657387

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.741657387 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.741657387 + -2
x = -3.741657387 + -2

Combine like terms: -3.741657387 + -2 = -5.741657387
x = -5.741657387

Simplifying
x = -5.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.741657387, -5.741657387}
Solution
x = {1.741657387, -5.741657387}

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