0.5(3x+10)(6x)=816

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Solution for 0.5(3x+10)(6x)=816 equation: 


Simplifying
0.5(3x + 10)(6x) = 816

Reorder the terms:
0.5(10 + 3x)(6x) = 816

Remove parenthesis around (6x)
0.5(10 + 3x) * 6x = 816

Reorder the terms for easier multiplication:
0.5 * 6x(10 + 3x) = 816

Multiply 0.5 * 6
3x(10 + 3x) = 816
(10 * 3x + 3x * 3x) = 816
(30x + 9x2) = 816

Solving
30x + 9x2 = 816

Solving for variable 'x'.

Reorder the terms:
-816 + 30x + 9x2 = 816 + -816

Combine like terms: 816 + -816 = 0
-816 + 30x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-272 + 10x + 3x2) = 0

Factor a trinomial.
3((-34 + -3x)(8 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-34 + -3x)' equal to zero and attempt to solve:

Simplifying
-34 + -3x = 0

Solving
-34 + -3x = 0

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

Add '34' to each side of the equation.
-34 + 34 + -3x = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -3x = 0 + 34
-3x = 0 + 34

Combine like terms: 0 + 34 = 34
-3x = 34

Divide each side by '-3'.
x = -11.33333333

Simplifying
x = -11.33333333

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-11.33333333, 8}

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