(x+3)(x-3)=(2x+5)(x-3)

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Solution for (x+3)(x-3)=(2x+5)(x-3) equation: 


Simplifying
(x + 3)(x + -3) = (2x + 5)(x + -3)

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

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

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

Combine like terms: 3x + -3x = 0
(-9 + 0 + x2) = (2x + 5)(x + -3)
(-9 + x2) = (2x + 5)(x + -3)

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

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

Multiply (5 + 2x) * (-3 + x)
-9 + x2 = (5(-3 + x) + 2x * (-3 + x))
-9 + x2 = ((-3 * 5 + x * 5) + 2x * (-3 + x))
-9 + x2 = ((-15 + 5x) + 2x * (-3 + x))
-9 + x2 = (-15 + 5x + (-3 * 2x + x * 2x))
-9 + x2 = (-15 + 5x + (-6x + 2x2))

Combine like terms: 5x + -6x = -1x
-9 + x2 = (-15 + -1x + 2x2)

Solving
-9 + x2 = -15 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-9 + 15 + x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: -9 + 15 = 6
6 + x + x2 + -2x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
6 + x + -1x2 = -15 + -1x + 2x2 + 15 + x + -2x2

Reorder the terms:
6 + x + -1x2 = -15 + 15 + -1x + x + 2x2 + -2x2

Combine like terms: -15 + 15 = 0
6 + x + -1x2 = 0 + -1x + x + 2x2 + -2x2
6 + x + -1x2 = -1x + x + 2x2 + -2x2

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

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

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


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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {3, -2}

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