(X+4)(X-5)=(2X+3)(X-5)

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Solution for (X+4)(X-5)=(2X+3)(X-5) equation: 


Simplifying
(X + 4)(X + -5) = (2X + 3)(X + -5)

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

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

Multiply (4 + X) * (-5 + X)
(4(-5 + X) + X(-5 + X)) = (2X + 3)(X + -5)
((-5 * 4 + X * 4) + X(-5 + X)) = (2X + 3)(X + -5)
((-20 + 4X) + X(-5 + X)) = (2X + 3)(X + -5)
(-20 + 4X + (-5 * X + X * X)) = (2X + 3)(X + -5)
(-20 + 4X + (-5X + X2)) = (2X + 3)(X + -5)

Combine like terms: 4X + -5X = -1X
(-20 + -1X + X2) = (2X + 3)(X + -5)

Reorder the terms:
-20 + -1X + X2 = (3 + 2X)(X + -5)

Reorder the terms:
-20 + -1X + X2 = (3 + 2X)(-5 + X)

Multiply (3 + 2X) * (-5 + X)
-20 + -1X + X2 = (3(-5 + X) + 2X * (-5 + X))
-20 + -1X + X2 = ((-5 * 3 + X * 3) + 2X * (-5 + X))
-20 + -1X + X2 = ((-15 + 3X) + 2X * (-5 + X))
-20 + -1X + X2 = (-15 + 3X + (-5 * 2X + X * 2X))
-20 + -1X + X2 = (-15 + 3X + (-10X + 2X2))

Combine like terms: 3X + -10X = -7X
-20 + -1X + X2 = (-15 + -7X + 2X2)

Solving
-20 + -1X + X2 = -15 + -7X + 2X2

Solving for variable 'X'.

Reorder the terms:
-20 + 15 + -1X + 7X + X2 + -2X2 = -15 + -7X + 2X2 + 15 + 7X + -2X2

Combine like terms: -20 + 15 = -5
-5 + -1X + 7X + X2 + -2X2 = -15 + -7X + 2X2 + 15 + 7X + -2X2

Combine like terms: -1X + 7X = 6X
-5 + 6X + X2 + -2X2 = -15 + -7X + 2X2 + 15 + 7X + -2X2

Combine like terms: X2 + -2X2 = -1X2
-5 + 6X + -1X2 = -15 + -7X + 2X2 + 15 + 7X + -2X2

Reorder the terms:
-5 + 6X + -1X2 = -15 + 15 + -7X + 7X + 2X2 + -2X2

Combine like terms: -15 + 15 = 0
-5 + 6X + -1X2 = 0 + -7X + 7X + 2X2 + -2X2
-5 + 6X + -1X2 = -7X + 7X + 2X2 + -2X2

Combine like terms: -7X + 7X = 0
-5 + 6X + -1X2 = 0 + 2X2 + -2X2
-5 + 6X + -1X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
-5 + 6X + -1X2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
X = {5, 1}

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