5(x-4)=3x(x-6)

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Solution for 5(x-4)=3x(x-6) equation: 


Simplifying
5(x + -4) = 3x(x + -6)

Reorder the terms:
5(-4 + x) = 3x(x + -6)
(-4 * 5 + x * 5) = 3x(x + -6)
(-20 + 5x) = 3x(x + -6)

Reorder the terms:
-20 + 5x = 3x(-6 + x)
-20 + 5x = (-6 * 3x + x * 3x)
-20 + 5x = (-18x + 3x2)

Solving
-20 + 5x = -18x + 3x2

Solving for variable 'x'.

Combine like terms: 5x + 18x = 23x
-20 + 23x + -3x2 = -18x + 3x2 + 18x + -3x2

Reorder the terms:
-20 + 23x + -3x2 = -18x + 18x + 3x2 + -3x2

Combine like terms: -18x + 18x = 0
-20 + 23x + -3x2 = 0 + 3x2 + -3x2
-20 + 23x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-20 + 23x + -3x2 = 0

Factor a trinomial.
(-20 + 3x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-20 + 3x)' equal to zero and attempt to solve:

Simplifying
-20 + 3x = 0

Solving
-20 + 3x = 0

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

Add '20' to each side of the equation.
-20 + 20 + 3x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3x = 0 + 20
3x = 0 + 20

Combine like terms: 0 + 20 = 20
3x = 20

Divide each side by '3'.
x = 6.666666667

Simplifying
x = 6.666666667

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 = {6.666666667, 1}

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