3(x^2-8)=2x(x+5)

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Solution for 3(x^2-8)=2x(x+5) equation: 


Simplifying
3(x2 + -8) = 2x(x + 5)

Reorder the terms:
3(-8 + x2) = 2x(x + 5)
(-8 * 3 + x2 * 3) = 2x(x + 5)
(-24 + 3x2) = 2x(x + 5)

Reorder the terms:
-24 + 3x2 = 2x(5 + x)
-24 + 3x2 = (5 * 2x + x * 2x)
-24 + 3x2 = (10x + 2x2)

Solving
-24 + 3x2 = 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
-24 + -10x + 3x2 + -2x2 = 10x + 2x2 + -10x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-24 + -10x + 1x2 = 10x + 2x2 + -10x + -2x2

Reorder the terms:
-24 + -10x + 1x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-24 + -10x + 1x2 = 0 + 2x2 + -2x2
-24 + -10x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-24 + -10x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(12 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}

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