3x(x+2)-5(x-3)=17

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Solution for 3x(x+2)-5(x-3)=17 equation: 


Simplifying
3x(x + 2) + -5(x + -3) = 17

Reorder the terms:
3x(2 + x) + -5(x + -3) = 17
(2 * 3x + x * 3x) + -5(x + -3) = 17
(6x + 3x2) + -5(x + -3) = 17

Reorder the terms:
6x + 3x2 + -5(-3 + x) = 17
6x + 3x2 + (-3 * -5 + x * -5) = 17
6x + 3x2 + (15 + -5x) = 17

Reorder the terms:
15 + 6x + -5x + 3x2 = 17

Combine like terms: 6x + -5x = 1x
15 + 1x + 3x2 = 17

Solving
15 + 1x + 3x2 = 17

Solving for variable 'x'.

Reorder the terms:
15 + -17 + 1x + 3x2 = 17 + -17

Combine like terms: 15 + -17 = -2
-2 + 1x + 3x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-2 + 1x + 3x2 = 0

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


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

Simplifying
-1 + -1x = 0

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

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 = {-1, 0.6666666667}

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