2x(x-5)=6x+66

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Solution for 2x(x-5)=6x+66 equation: 


Simplifying
2x(x + -5) = 6x + 66

Reorder the terms:
2x(-5 + x) = 6x + 66
(-5 * 2x + x * 2x) = 6x + 66
(-10x + 2x2) = 6x + 66

Reorder the terms:
-10x + 2x2 = 66 + 6x

Solving
-10x + 2x2 = 66 + 6x

Solving for variable 'x'.

Reorder the terms:
-66 + -10x + -6x + 2x2 = 66 + 6x + -66 + -6x

Combine like terms: -10x + -6x = -16x
-66 + -16x + 2x2 = 66 + 6x + -66 + -6x

Reorder the terms:
-66 + -16x + 2x2 = 66 + -66 + 6x + -6x

Combine like terms: 66 + -66 = 0
-66 + -16x + 2x2 = 0 + 6x + -6x
-66 + -16x + 2x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-66 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -8x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(11 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-3, 11}

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