(3x^2-7x+1)+3x(x+4)=

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Solution for (3x^2-7x+1)+3x(x+4)= equation: 


Simplifying
(3x2 + -7x + 1) + 3x(x + 4) = 0

Reorder the terms:
(1 + -7x + 3x2) + 3x(x + 4) = 0

Remove parenthesis around (1 + -7x + 3x2)
1 + -7x + 3x2 + 3x(x + 4) = 0

Reorder the terms:
1 + -7x + 3x2 + 3x(4 + x) = 0
1 + -7x + 3x2 + (4 * 3x + x * 3x) = 0
1 + -7x + 3x2 + (12x + 3x2) = 0

Reorder the terms:
1 + -7x + 12x + 3x2 + 3x2 = 0

Combine like terms: -7x + 12x = 5x
1 + 5x + 3x2 + 3x2 = 0

Combine like terms: 3x2 + 3x2 = 6x2
1 + 5x + 6x2 = 0

Solving
1 + 5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + 2x)(1 + 3x) = 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 '(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
Solution
x = {-0.5, -0.3333333333}

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