x^2-x=(2x+7)(x-5)

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Solution for x^2-x=(2x+7)(x-5) equation: 


Simplifying
x2 + -1x = (2x + 7)(x + -5)

Reorder the terms:
-1x + x2 = (2x + 7)(x + -5)

Reorder the terms:
-1x + x2 = (7 + 2x)(x + -5)

Reorder the terms:
-1x + x2 = (7 + 2x)(-5 + x)

Multiply (7 + 2x) * (-5 + x)
-1x + x2 = (7(-5 + x) + 2x * (-5 + x))
-1x + x2 = ((-5 * 7 + x * 7) + 2x * (-5 + x))
-1x + x2 = ((-35 + 7x) + 2x * (-5 + x))
-1x + x2 = (-35 + 7x + (-5 * 2x + x * 2x))
-1x + x2 = (-35 + 7x + (-10x + 2x2))

Combine like terms: 7x + -10x = -3x
-1x + x2 = (-35 + -3x + 2x2)

Solving
-1x + x2 = -35 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
35 + -1x + 3x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: -1x + 3x = 2x
35 + 2x + x2 + -2x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
35 + 2x + -1x2 = -35 + -3x + 2x2 + 35 + 3x + -2x2

Reorder the terms:
35 + 2x + -1x2 = -35 + 35 + -3x + 3x + 2x2 + -2x2

Combine like terms: -35 + 35 = 0
35 + 2x + -1x2 = 0 + -3x + 3x + 2x2 + -2x2
35 + 2x + -1x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
35 + 2x + -1x2 = 0 + 2x2 + -2x2
35 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
35 + 2x + -1x2 = 0

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


Subproblem 1
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

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

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {7, -5}

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