10800=3x(2x+1)12

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


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

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

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

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

Solving
10800 = 36x + 72x2

Solving for variable 'x'.

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

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

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

Factor out the Greatest Common Factor (GCF), '36'.
36(300 + -1x + -2x2) = 0

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

Ignore the factor 36.

Subproblem 1

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

Subproblem 2

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

Solution

x = {12, -12.5}

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