(2x+3)(x-6)=17

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Solution for (2x+3)(x-6)=17 equation: 


Simplifying
(2x + 3)(x + -6) = 17

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

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

Multiply (3 + 2x) * (-6 + x)
(3(-6 + x) + 2x * (-6 + x)) = 17
((-6 * 3 + x * 3) + 2x * (-6 + x)) = 17
((-18 + 3x) + 2x * (-6 + x)) = 17
(-18 + 3x + (-6 * 2x + x * 2x)) = 17
(-18 + 3x + (-12x + 2x2)) = 17

Combine like terms: 3x + -12x = -9x
(-18 + -9x + 2x2) = 17

Solving
-18 + -9x + 2x2 = 17

Solving for variable 'x'.

Reorder the terms:
-18 + -17 + -9x + 2x2 = 17 + -17

Combine like terms: -18 + -17 = -35
-35 + -9x + 2x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-35 + -9x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2.5, 7}

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