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

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Solution for (3x-2)(5x+2)+1=0 equation: 


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

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

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

Multiply (-2 + 3x) * (2 + 5x)
(-2(2 + 5x) + 3x * (2 + 5x)) + 1 = 0
((2 * -2 + 5x * -2) + 3x * (2 + 5x)) + 1 = 0
((-4 + -10x) + 3x * (2 + 5x)) + 1 = 0
(-4 + -10x + (2 * 3x + 5x * 3x)) + 1 = 0
(-4 + -10x + (6x + 15x2)) + 1 = 0

Combine like terms: -10x + 6x = -4x
(-4 + -4x + 15x2) + 1 = 0

Reorder the terms:
-4 + 1 + -4x + 15x2 = 0

Combine like terms: -4 + 1 = -3
-3 + -4x + 15x2 = 0

Solving
-3 + -4x + 15x2 = 0

Solving for variable 'x'.

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

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {-0.3333333333, 0.6}

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