(2x+3)(x-5)-24=(x+4)(x-9)

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Solution for (2x+3)(x-5)-24=(x+4)(x-9) equation:


Simplifying
(2x + 3)(x + -5) + -24 = (x + 4)(x + -9)

Reorder the terms:
(3 + 2x)(x + -5) + -24 = (x + 4)(x + -9)

Reorder the terms:
(3 + 2x)(-5 + x) + -24 = (x + 4)(x + -9)

Multiply (3 + 2x) * (-5 + x)
(3(-5 + x) + 2x * (-5 + x)) + -24 = (x + 4)(x + -9)
((-5 * 3 + x * 3) + 2x * (-5 + x)) + -24 = (x + 4)(x + -9)
((-15 + 3x) + 2x * (-5 + x)) + -24 = (x + 4)(x + -9)
(-15 + 3x + (-5 * 2x + x * 2x)) + -24 = (x + 4)(x + -9)
(-15 + 3x + (-10x + 2x2)) + -24 = (x + 4)(x + -9)

Combine like terms: 3x + -10x = -7x
(-15 + -7x + 2x2) + -24 = (x + 4)(x + -9)

Reorder the terms:
-15 + -24 + -7x + 2x2 = (x + 4)(x + -9)

Combine like terms: -15 + -24 = -39
-39 + -7x + 2x2 = (x + 4)(x + -9)

Reorder the terms:
-39 + -7x + 2x2 = (4 + x)(x + -9)

Reorder the terms:
-39 + -7x + 2x2 = (4 + x)(-9 + x)

Multiply (4 + x) * (-9 + x)
-39 + -7x + 2x2 = (4(-9 + x) + x(-9 + x))
-39 + -7x + 2x2 = ((-9 * 4 + x * 4) + x(-9 + x))
-39 + -7x + 2x2 = ((-36 + 4x) + x(-9 + x))
-39 + -7x + 2x2 = (-36 + 4x + (-9 * x + x * x))
-39 + -7x + 2x2 = (-36 + 4x + (-9x + x2))

Combine like terms: 4x + -9x = -5x
-39 + -7x + 2x2 = (-36 + -5x + x2)

Solving
-39 + -7x + 2x2 = -36 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
-39 + 36 + -7x + 5x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: -39 + 36 = -3
-3 + -7x + 5x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: -7x + 5x = -2x
-3 + -2x + 2x2 + -1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-3 + -2x + 1x2 = -36 + -5x + x2 + 36 + 5x + -1x2

Reorder the terms:
-3 + -2x + 1x2 = -36 + 36 + -5x + 5x + x2 + -1x2

Combine like terms: -36 + 36 = 0
-3 + -2x + 1x2 = 0 + -5x + 5x + x2 + -1x2
-3 + -2x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-3 + -2x + 1x2 = 0 + x2 + -1x2
-3 + -2x + 1x2 = x2 + -1x2

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-1, 3}

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