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

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


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

Reorder the terms:
5x(-2 + x) = 6 + 3x
(-2 * 5x + x * 5x) = 6 + 3x
(-10x + 5x2) = 6 + 3x

Solving
-10x + 5x2 = 6 + 3x

Solving for variable 'x'.

Reorder the terms:
-6 + -10x + -3x + 5x2 = 6 + 3x + -6 + -3x

Combine like terms: -10x + -3x = -13x
-6 + -13x + 5x2 = 6 + 3x + -6 + -3x

Reorder the terms:
-6 + -13x + 5x2 = 6 + -6 + 3x + -3x

Combine like terms: 6 + -6 = 0
-6 + -13x + 5x2 = 0 + 3x + -3x
-6 + -13x + 5x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + -13x + 5x2 = 0

Factor a trinomial.
(-2 + -5x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
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
Solution
x = {-0.4, 3}

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