3x(x+5)=6(x-5)

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Solution for 3x(x+5)=6(x-5) equation: 


Simplifying
3x(x + 5) = 6(x + -5)

Reorder the terms:
3x(5 + x) = 6(x + -5)
(5 * 3x + x * 3x) = 6(x + -5)
(15x + 3x2) = 6(x + -5)

Reorder the terms:
15x + 3x2 = 6(-5 + x)
15x + 3x2 = (-5 * 6 + x * 6)
15x + 3x2 = (-30 + 6x)

Solving
15x + 3x2 = -30 + 6x

Solving for variable 'x'.

Reorder the terms:
30 + 15x + -6x + 3x2 = -30 + 6x + 30 + -6x

Combine like terms: 15x + -6x = 9x
30 + 9x + 3x2 = -30 + 6x + 30 + -6x

Reorder the terms:
30 + 9x + 3x2 = -30 + 30 + 6x + -6x

Combine like terms: -30 + 30 = 0
30 + 9x + 3x2 = 0 + 6x + -6x
30 + 9x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
30 + 9x + 3x2 = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(10 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 3x + x2 = 0

Solving
10 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x + x2 = 0 + -10
3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
3x + x2 = -10

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -10 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + 3x + x2 = -7.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -7.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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