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

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


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

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

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

Multiply (-3 + 5x) * (1 + 3x)
(-3(1 + 3x) + 5x * (1 + 3x)) = 1
((1 * -3 + 3x * -3) + 5x * (1 + 3x)) = 1
((-3 + -9x) + 5x * (1 + 3x)) = 1
(-3 + -9x + (1 * 5x + 3x * 5x)) = 1
(-3 + -9x + (5x + 15x2)) = 1

Combine like terms: -9x + 5x = -4x
(-3 + -4x + 15x2) = 1

Solving
-3 + -4x + 15x2 = 1

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + -4x + 15x2 = 1 + -1

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

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

Factor a trinomial.
(-2 + -5x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-2 + -5x)' equal to zero and attempt to solve:

Simplifying
-2 + -5x = 0

Solving
-2 + -5x = 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 + -5x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5x = 0 + 2
-5x = 0 + 2

Combine like terms: 0 + 2 = 2
-5x = 2

Divide each side by '-5'.
x = -0.4

Simplifying
x = -0.4

Subproblem 2
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
Solution
x = {-0.4, 0.6666666667}

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