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

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


Simplifying
0 = (3x + -2)(5x + 1)

Reorder the terms:
0 = (-2 + 3x)(5x + 1)

Reorder the terms:
0 = (-2 + 3x)(1 + 5x)

Multiply (-2 + 3x) * (1 + 5x)
0 = (-2(1 + 5x) + 3x * (1 + 5x))
0 = ((1 * -2 + 5x * -2) + 3x * (1 + 5x))
0 = ((-2 + -10x) + 3x * (1 + 5x))
0 = (-2 + -10x + (1 * 3x + 5x * 3x))
0 = (-2 + -10x + (3x + 15x2))

Combine like terms: -10x + 3x = -7x
0 = (-2 + -7x + 15x2)

Solving
0 = -2 + -7x + 15x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + 7x + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2

Reorder the terms:
2 + 7x + -15x2 = -2 + 2 + -7x + 7x + 15x2 + -15x2

Combine like terms: -2 + 2 = 0
2 + 7x + -15x2 = 0 + -7x + 7x + 15x2 + -15x2
2 + 7x + -15x2 = -7x + 7x + 15x2 + -15x2

Combine like terms: -7x + 7x = 0
2 + 7x + -15x2 = 0 + 15x2 + -15x2
2 + 7x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
2 + 7x + -15x2 = 0

Factor a trinomial.
(2 + -3x)(1 + 5x) = 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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 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 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2
Solution
x = {0.6666666667, -0.2}

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