4x^2-17x+10=x(x-6)

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Solution for 4x^2-17x+10=x(x-6) equation: 


Simplifying
4x2 + -17x + 10 = x(x + -6)

Reorder the terms:
10 + -17x + 4x2 = x(x + -6)

Reorder the terms:
10 + -17x + 4x2 = x(-6 + x)
10 + -17x + 4x2 = (-6 * x + x * x)
10 + -17x + 4x2 = (-6x + x2)

Solving
10 + -17x + 4x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
10 + -17x + 6x + 4x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -17x + 6x = -11x
10 + -11x + 4x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
10 + -11x + 3x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
10 + -11x + 3x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
10 + -11x + 3x2 = 0 + x2 + -1x2
10 + -11x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -11x + 3x2 = 0

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


Subproblem 1
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

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.666666667, 2}

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