(x+2)(x-5)=(2x+9)(x-5)

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Solution for (x+2)(x-5)=(2x+9)(x-5) equation: 


Simplifying
(x + 2)(x + -5) = (2x + 9)(x + -5)

Reorder the terms:
(2 + x)(x + -5) = (2x + 9)(x + -5)

Reorder the terms:
(2 + x)(-5 + x) = (2x + 9)(x + -5)

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = (2x + 9)(x + -5)
((-5 * 2 + x * 2) + x(-5 + x)) = (2x + 9)(x + -5)
((-10 + 2x) + x(-5 + x)) = (2x + 9)(x + -5)
(-10 + 2x + (-5 * x + x * x)) = (2x + 9)(x + -5)
(-10 + 2x + (-5x + x2)) = (2x + 9)(x + -5)

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = (2x + 9)(x + -5)

Reorder the terms:
-10 + -3x + x2 = (9 + 2x)(x + -5)

Reorder the terms:
-10 + -3x + x2 = (9 + 2x)(-5 + x)

Multiply (9 + 2x) * (-5 + x)
-10 + -3x + x2 = (9(-5 + x) + 2x * (-5 + x))
-10 + -3x + x2 = ((-5 * 9 + x * 9) + 2x * (-5 + x))
-10 + -3x + x2 = ((-45 + 9x) + 2x * (-5 + x))
-10 + -3x + x2 = (-45 + 9x + (-5 * 2x + x * 2x))
-10 + -3x + x2 = (-45 + 9x + (-10x + 2x2))

Combine like terms: 9x + -10x = -1x
-10 + -3x + x2 = (-45 + -1x + 2x2)

Solving
-10 + -3x + x2 = -45 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-10 + 45 + -3x + x + x2 + -2x2 = -45 + -1x + 2x2 + 45 + x + -2x2

Combine like terms: -10 + 45 = 35
35 + -3x + x + x2 + -2x2 = -45 + -1x + 2x2 + 45 + x + -2x2

Combine like terms: -3x + x = -2x
35 + -2x + x2 + -2x2 = -45 + -1x + 2x2 + 45 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
35 + -2x + -1x2 = -45 + -1x + 2x2 + 45 + x + -2x2

Reorder the terms:
35 + -2x + -1x2 = -45 + 45 + -1x + x + 2x2 + -2x2

Combine like terms: -45 + 45 = 0
35 + -2x + -1x2 = 0 + -1x + x + 2x2 + -2x2
35 + -2x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 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.
(5 + -1x)(7 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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

Simplifying
7 + x = 0

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

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

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

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

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