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

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


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

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

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

Multiply (9 + x) * (-2 + x)
(9(-2 + x) + x(-2 + x)) = (2x + 5)(x + -2)
((-2 * 9 + x * 9) + x(-2 + x)) = (2x + 5)(x + -2)
((-18 + 9x) + x(-2 + x)) = (2x + 5)(x + -2)
(-18 + 9x + (-2 * x + x * x)) = (2x + 5)(x + -2)
(-18 + 9x + (-2x + x2)) = (2x + 5)(x + -2)

Combine like terms: 9x + -2x = 7x
(-18 + 7x + x2) = (2x + 5)(x + -2)

Reorder the terms:
-18 + 7x + x2 = (5 + 2x)(x + -2)

Reorder the terms:
-18 + 7x + x2 = (5 + 2x)(-2 + x)

Multiply (5 + 2x) * (-2 + x)
-18 + 7x + x2 = (5(-2 + x) + 2x * (-2 + x))
-18 + 7x + x2 = ((-2 * 5 + x * 5) + 2x * (-2 + x))
-18 + 7x + x2 = ((-10 + 5x) + 2x * (-2 + x))
-18 + 7x + x2 = (-10 + 5x + (-2 * 2x + x * 2x))
-18 + 7x + x2 = (-10 + 5x + (-4x + 2x2))

Combine like terms: 5x + -4x = 1x
-18 + 7x + x2 = (-10 + 1x + 2x2)

Solving
-18 + 7x + x2 = -10 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 10 + 7x + -1x + x2 + -2x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Combine like terms: -18 + 10 = -8
-8 + 7x + -1x + x2 + -2x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Combine like terms: 7x + -1x = 6x
-8 + 6x + x2 + -2x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-8 + 6x + -1x2 = -10 + 1x + 2x2 + 10 + -1x + -2x2

Reorder the terms:
-8 + 6x + -1x2 = -10 + 10 + 1x + -1x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
-8 + 6x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2
-8 + 6x + -1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
-8 + 6x + -1x2 = 0 + 2x2 + -2x2
-8 + 6x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + 6x + -1x2 = 0

Factor a trinomial.
(-4 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {4, 2}

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