3x(x-1)=5(x-1)

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Solution for 3x(x-1)=5(x-1) equation: 


Simplifying
3x(x + -1) = 5(x + -1)

Reorder the terms:
3x(-1 + x) = 5(x + -1)
(-1 * 3x + x * 3x) = 5(x + -1)
(-3x + 3x2) = 5(x + -1)

Reorder the terms:
-3x + 3x2 = 5(-1 + x)
-3x + 3x2 = (-1 * 5 + x * 5)
-3x + 3x2 = (-5 + 5x)

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

Solving for variable 'x'.

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

Combine like terms: -3x + -5x = -8x
5 + -8x + 3x2 = -5 + 5x + 5 + -5x

Reorder the terms:
5 + -8x + 3x2 = -5 + 5 + 5x + -5x

Combine like terms: -5 + 5 = 0
5 + -8x + 3x2 = 0 + 5x + -5x
5 + -8x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
5 + -8x + 3x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {1, 1.666666667}

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