(2x+1)(x-7)=17

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Solution for (2x+1)(x-7)=17 equation: 


Simplifying
(2x + 1)(x + -7) = 17

Reorder the terms:
(1 + 2x)(x + -7) = 17

Reorder the terms:
(1 + 2x)(-7 + x) = 17

Multiply (1 + 2x) * (-7 + x)
(1(-7 + x) + 2x * (-7 + x)) = 17
((-7 * 1 + x * 1) + 2x * (-7 + x)) = 17
((-7 + 1x) + 2x * (-7 + x)) = 17
(-7 + 1x + (-7 * 2x + x * 2x)) = 17
(-7 + 1x + (-14x + 2x2)) = 17

Combine like terms: 1x + -14x = -13x
(-7 + -13x + 2x2) = 17

Solving
-7 + -13x + 2x2 = 17

Solving for variable 'x'.

Reorder the terms:
-7 + -17 + -13x + 2x2 = 17 + -17

Combine like terms: -7 + -17 = -24
-24 + -13x + 2x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-24 + -13x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1.5, 8}

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