6x(5-x)=3(2x+6)

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Solution for 6x(5-x)=3(2x+6) equation:


Simplifying
6x(5 + -1x) = 3(2x + 6)
(5 * 6x + -1x * 6x) = 3(2x + 6)
(30x + -6x2) = 3(2x + 6)

Reorder the terms:
30x + -6x2 = 3(6 + 2x)
30x + -6x2 = (6 * 3 + 2x * 3)
30x + -6x2 = (18 + 6x)

Solving
30x + -6x2 = 18 + 6x

Solving for variable 'x'.

Reorder the terms:
-18 + 30x + -6x + -6x2 = 18 + 6x + -18 + -6x

Combine like terms: 30x + -6x = 24x
-18 + 24x + -6x2 = 18 + 6x + -18 + -6x

Reorder the terms:
-18 + 24x + -6x2 = 18 + -18 + 6x + -6x

Combine like terms: 18 + -18 = 0
-18 + 24x + -6x2 = 0 + 6x + -6x
-18 + 24x + -6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-18 + 24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 4x + -1x2) = 0

Factor a trinomial.
6((-3 + x)(1 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

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

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

Simplifying
x = 3

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}

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