(3x+4)(x-9)=(x-17)(2x+3)

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Solution for (3x+4)(x-9)=(x-17)(2x+3) equation: 


Simplifying
(3x + 4)(x + -9) = (x + -17)(2x + 3)

Reorder the terms:
(4 + 3x)(x + -9) = (x + -17)(2x + 3)

Reorder the terms:
(4 + 3x)(-9 + x) = (x + -17)(2x + 3)

Multiply (4 + 3x) * (-9 + x)
(4(-9 + x) + 3x * (-9 + x)) = (x + -17)(2x + 3)
((-9 * 4 + x * 4) + 3x * (-9 + x)) = (x + -17)(2x + 3)
((-36 + 4x) + 3x * (-9 + x)) = (x + -17)(2x + 3)
(-36 + 4x + (-9 * 3x + x * 3x)) = (x + -17)(2x + 3)
(-36 + 4x + (-27x + 3x2)) = (x + -17)(2x + 3)

Combine like terms: 4x + -27x = -23x
(-36 + -23x + 3x2) = (x + -17)(2x + 3)

Reorder the terms:
-36 + -23x + 3x2 = (-17 + x)(2x + 3)

Reorder the terms:
-36 + -23x + 3x2 = (-17 + x)(3 + 2x)

Multiply (-17 + x) * (3 + 2x)
-36 + -23x + 3x2 = (-17(3 + 2x) + x(3 + 2x))
-36 + -23x + 3x2 = ((3 * -17 + 2x * -17) + x(3 + 2x))
-36 + -23x + 3x2 = ((-51 + -34x) + x(3 + 2x))
-36 + -23x + 3x2 = (-51 + -34x + (3 * x + 2x * x))
-36 + -23x + 3x2 = (-51 + -34x + (3x + 2x2))

Combine like terms: -34x + 3x = -31x
-36 + -23x + 3x2 = (-51 + -31x + 2x2)

Solving
-36 + -23x + 3x2 = -51 + -31x + 2x2

Solving for variable 'x'.

Reorder the terms:
-36 + 51 + -23x + 31x + 3x2 + -2x2 = -51 + -31x + 2x2 + 51 + 31x + -2x2

Combine like terms: -36 + 51 = 15
15 + -23x + 31x + 3x2 + -2x2 = -51 + -31x + 2x2 + 51 + 31x + -2x2

Combine like terms: -23x + 31x = 8x
15 + 8x + 3x2 + -2x2 = -51 + -31x + 2x2 + 51 + 31x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
15 + 8x + 1x2 = -51 + -31x + 2x2 + 51 + 31x + -2x2

Reorder the terms:
15 + 8x + 1x2 = -51 + 51 + -31x + 31x + 2x2 + -2x2

Combine like terms: -51 + 51 = 0
15 + 8x + 1x2 = 0 + -31x + 31x + 2x2 + -2x2
15 + 8x + 1x2 = -31x + 31x + 2x2 + -2x2

Combine like terms: -31x + 31x = 0
15 + 8x + 1x2 = 0 + 2x2 + -2x2
15 + 8x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
15 + 8x + 1x2 = 0

Factor a trinomial.
(5 + x)(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {-5, -3}

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