6x^2-15x+10=6x+1

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Solution for 6x^2-15x+10=6x+1 equation: 


Simplifying
6x2 + -15x + 10 = 6x + 1

Reorder the terms:
10 + -15x + 6x2 = 6x + 1

Reorder the terms:
10 + -15x + 6x2 = 1 + 6x

Solving
10 + -15x + 6x2 = 1 + 6x

Solving for variable 'x'.

Reorder the terms:
10 + -1 + -15x + -6x + 6x2 = 1 + 6x + -1 + -6x

Combine like terms: 10 + -1 = 9
9 + -15x + -6x + 6x2 = 1 + 6x + -1 + -6x

Combine like terms: -15x + -6x = -21x
9 + -21x + 6x2 = 1 + 6x + -1 + -6x

Reorder the terms:
9 + -21x + 6x2 = 1 + -1 + 6x + -6x

Combine like terms: 1 + -1 = 0
9 + -21x + 6x2 = 0 + 6x + -6x
9 + -21x + 6x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
9 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -7x + 2x2) = 0

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

Ignore the factor 3.

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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}

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