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

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


Simplifying
6(x2 + -2x) = -1x + 10

Reorder the terms:
6(-2x + x2) = -1x + 10
(-2x * 6 + x2 * 6) = -1x + 10
(-12x + 6x2) = -1x + 10

Reorder the terms:
-12x + 6x2 = 10 + -1x

Solving
-12x + 6x2 = 10 + -1x

Solving for variable 'x'.

Reorder the terms:
-10 + -12x + x + 6x2 = 10 + -1x + -10 + x

Combine like terms: -12x + x = -11x
-10 + -11x + 6x2 = 10 + -1x + -10 + x

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

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

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

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


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.6666666667, 2.5}

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