2(3x^2-10x+4)=3x+1

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Solution for 2(3x^2-10x+4)=3x+1 equation: 


Simplifying
2(3x2 + -10x + 4) = 3x + 1

Reorder the terms:
2(4 + -10x + 3x2) = 3x + 1
(4 * 2 + -10x * 2 + 3x2 * 2) = 3x + 1
(8 + -20x + 6x2) = 3x + 1

Reorder the terms:
8 + -20x + 6x2 = 1 + 3x

Solving
8 + -20x + 6x2 = 1 + 3x

Solving for variable 'x'.

Reorder the terms:
8 + -1 + -20x + -3x + 6x2 = 1 + 3x + -1 + -3x

Combine like terms: 8 + -1 = 7
7 + -20x + -3x + 6x2 = 1 + 3x + -1 + -3x

Combine like terms: -20x + -3x = -23x
7 + -23x + 6x2 = 1 + 3x + -1 + -3x

Reorder the terms:
7 + -23x + 6x2 = 1 + -1 + 3x + -3x

Combine like terms: 1 + -1 = 0
7 + -23x + 6x2 = 0 + 3x + -3x
7 + -23x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
7 + -23x + 6x2 = 0

Factor a trinomial.
(1 + -3x)(7 + -2x) = 0


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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {0.3333333333, 3.5}

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