(3x)(2x+1)(12)=10800

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Solution for (3x)(2x+1)(12)=10800 equation: 


Simplifying
(3x)(2x + 1)(12) = 10800

Remove parenthesis around (3x)
3x(2x + 1)(12) = 10800

Reorder the terms:
3x(1 + 2x)(12) = 10800

Reorder the terms for easier multiplication:
3 * 12x(1 + 2x) = 10800

Multiply 3 * 12
36x(1 + 2x) = 10800
(1 * 36x + 2x * 36x) = 10800
(36x + 72x2) = 10800

Solving
36x + 72x2 = 10800

Solving for variable 'x'.

Reorder the terms:
-10800 + 36x + 72x2 = 10800 + -10800

Combine like terms: 10800 + -10800 = 0
-10800 + 36x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '36'.
36(-300 + x + 2x2) = 0

Factor a trinomial.
36((-25 + -2x)(12 + -1x)) = 0

Ignore the factor 36.

Subproblem 1
Set the factor '(-25 + -2x)' equal to zero and attempt to solve:

Simplifying
-25 + -2x = 0

Solving
-25 + -2x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x = 0 + 25
-2x = 0 + 25

Combine like terms: 0 + 25 = 25
-2x = 25

Divide each side by '-2'.
x = -12.5

Simplifying
x = -12.5

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 = {-12.5, 12}

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