3x*(2x+5)-(x+3)*(3x-1)=1

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Solution for 3x*(2x+5)-(x+3)*(3x-1)=1 equation: 


Simplifying
3x(2x + 5) + -1(x + 3)(3x + -1) = 1

Reorder the terms:
3x(5 + 2x) + -1(x + 3)(3x + -1) = 1
(5 * 3x + 2x * 3x) + -1(x + 3)(3x + -1) = 1
(15x + 6x2) + -1(x + 3)(3x + -1) = 1

Reorder the terms:
15x + 6x2 + -1(3 + x)(3x + -1) = 1

Reorder the terms:
15x + 6x2 + -1(3 + x)(-1 + 3x) = 1

Multiply (3 + x) * (-1 + 3x)
15x + 6x2 + -1(3(-1 + 3x) + x(-1 + 3x)) = 1
15x + 6x2 + -1((-1 * 3 + 3x * 3) + x(-1 + 3x)) = 1
15x + 6x2 + -1((-3 + 9x) + x(-1 + 3x)) = 1
15x + 6x2 + -1(-3 + 9x + (-1 * x + 3x * x)) = 1
15x + 6x2 + -1(-3 + 9x + (-1x + 3x2)) = 1

Combine like terms: 9x + -1x = 8x
15x + 6x2 + -1(-3 + 8x + 3x2) = 1
15x + 6x2 + (-3 * -1 + 8x * -1 + 3x2 * -1) = 1
15x + 6x2 + (3 + -8x + -3x2) = 1

Reorder the terms:
3 + 15x + -8x + 6x2 + -3x2 = 1

Combine like terms: 15x + -8x = 7x
3 + 7x + 6x2 + -3x2 = 1

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

Solving
3 + 7x + 3x2 = 1

Solving for variable 'x'.

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

Combine like terms: 3 + -1 = 2
2 + 7x + 3x2 = 1 + -1

Combine like terms: 1 + -1 = 0
2 + 7x + 3x2 = 0

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


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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

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 = {-2, -0.3333333333}

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