(2x-3)(3x+1)=17

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Solution for (2x-3)(3x+1)=17 equation: 


Simplifying
(2x + -3)(3x + 1) = 17

Reorder the terms:
(-3 + 2x)(3x + 1) = 17

Reorder the terms:
(-3 + 2x)(1 + 3x) = 17

Multiply (-3 + 2x) * (1 + 3x)
(-3(1 + 3x) + 2x * (1 + 3x)) = 17
((1 * -3 + 3x * -3) + 2x * (1 + 3x)) = 17
((-3 + -9x) + 2x * (1 + 3x)) = 17
(-3 + -9x + (1 * 2x + 3x * 2x)) = 17
(-3 + -9x + (2x + 6x2)) = 17

Combine like terms: -9x + 2x = -7x
(-3 + -7x + 6x2) = 17

Solving
-3 + -7x + 6x2 = 17

Solving for variable 'x'.

Reorder the terms:
-3 + -17 + -7x + 6x2 = 17 + -17

Combine like terms: -3 + -17 = -20
-20 + -7x + 6x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-20 + -7x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

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

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

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-1.333333333, 2.5}

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