3x(10x+x-8)=21x(x-8)

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Solution for 3x(10x+x-8)=21x(x-8) equation: 


Simplifying
3x(10x + x + -8) = 21x(x + -8)

Reorder the terms:
3x(-8 + 10x + x) = 21x(x + -8)

Combine like terms: 10x + x = 11x
3x(-8 + 11x) = 21x(x + -8)
(-8 * 3x + 11x * 3x) = 21x(x + -8)
(-24x + 33x2) = 21x(x + -8)

Reorder the terms:
-24x + 33x2 = 21x(-8 + x)
-24x + 33x2 = (-8 * 21x + x * 21x)
-24x + 33x2 = (-168x + 21x2)

Solving
-24x + 33x2 = -168x + 21x2

Solving for variable 'x'.

Reorder the terms:
-24x + 168x + 33x2 + -21x2 = -168x + 21x2 + 168x + -21x2

Combine like terms: -24x + 168x = 144x
144x + 33x2 + -21x2 = -168x + 21x2 + 168x + -21x2

Combine like terms: 33x2 + -21x2 = 12x2
144x + 12x2 = -168x + 21x2 + 168x + -21x2

Reorder the terms:
144x + 12x2 = -168x + 168x + 21x2 + -21x2

Combine like terms: -168x + 168x = 0
144x + 12x2 = 0 + 21x2 + -21x2
144x + 12x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
144x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '12x'.
12x(12 + x) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
12 + x = 0

Solving
12 + x = 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 + x = 0 + -12

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

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

Simplifying
x = -12
Solution
x = {0, -12}

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