3x^2-15x+5=x(x-4)

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Solution for 3x^2-15x+5=x(x-4) equation: 


Simplifying
3x2 + -15x + 5 = x(x + -4)

Reorder the terms:
5 + -15x + 3x2 = x(x + -4)

Reorder the terms:
5 + -15x + 3x2 = x(-4 + x)
5 + -15x + 3x2 = (-4 * x + x * x)
5 + -15x + 3x2 = (-4x + x2)

Solving
5 + -15x + 3x2 = -4x + x2

Solving for variable 'x'.

Reorder the terms:
5 + -15x + 4x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: -15x + 4x = -11x
5 + -11x + 3x2 + -1x2 = -4x + x2 + 4x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
5 + -11x + 2x2 = -4x + x2 + 4x + -1x2

Reorder the terms:
5 + -11x + 2x2 = -4x + 4x + x2 + -1x2

Combine like terms: -4x + 4x = 0
5 + -11x + 2x2 = 0 + x2 + -1x2
5 + -11x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + -11x + 2x2 = 0

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


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0.5, 5}

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