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

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


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

Reorder the terms:
(-2 + 2x)(x + 5) = 17x + -17

Reorder the terms:
(-2 + 2x)(5 + x) = 17x + -17

Multiply (-2 + 2x) * (5 + x)
(-2(5 + x) + 2x * (5 + x)) = 17x + -17
((5 * -2 + x * -2) + 2x * (5 + x)) = 17x + -17
((-10 + -2x) + 2x * (5 + x)) = 17x + -17
(-10 + -2x + (5 * 2x + x * 2x)) = 17x + -17
(-10 + -2x + (10x + 2x2)) = 17x + -17

Combine like terms: -2x + 10x = 8x
(-10 + 8x + 2x2) = 17x + -17

Reorder the terms:
-10 + 8x + 2x2 = -17 + 17x

Solving
-10 + 8x + 2x2 = -17 + 17x

Solving for variable 'x'.

Reorder the terms:
-10 + 17 + 8x + -17x + 2x2 = -17 + 17x + 17 + -17x

Combine like terms: -10 + 17 = 7
7 + 8x + -17x + 2x2 = -17 + 17x + 17 + -17x

Combine like terms: 8x + -17x = -9x
7 + -9x + 2x2 = -17 + 17x + 17 + -17x

Reorder the terms:
7 + -9x + 2x2 = -17 + 17 + 17x + -17x

Combine like terms: -17 + 17 = 0
7 + -9x + 2x2 = 0 + 17x + -17x
7 + -9x + 2x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
7 + -9x + 2x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -2x) = 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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1, 3.5}

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