(3x+8)(x-5)=12x+32

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Solution for (3x+8)(x-5)=12x+32 equation: 


Simplifying
(3x + 8)(x + -5) = 12x + 32

Reorder the terms:
(8 + 3x)(x + -5) = 12x + 32

Reorder the terms:
(8 + 3x)(-5 + x) = 12x + 32

Multiply (8 + 3x) * (-5 + x)
(8(-5 + x) + 3x * (-5 + x)) = 12x + 32
((-5 * 8 + x * 8) + 3x * (-5 + x)) = 12x + 32
((-40 + 8x) + 3x * (-5 + x)) = 12x + 32
(-40 + 8x + (-5 * 3x + x * 3x)) = 12x + 32
(-40 + 8x + (-15x + 3x2)) = 12x + 32

Combine like terms: 8x + -15x = -7x
(-40 + -7x + 3x2) = 12x + 32

Reorder the terms:
-40 + -7x + 3x2 = 32 + 12x

Solving
-40 + -7x + 3x2 = 32 + 12x

Solving for variable 'x'.

Reorder the terms:
-40 + -32 + -7x + -12x + 3x2 = 32 + 12x + -32 + -12x

Combine like terms: -40 + -32 = -72
-72 + -7x + -12x + 3x2 = 32 + 12x + -32 + -12x

Combine like terms: -7x + -12x = -19x
-72 + -19x + 3x2 = 32 + 12x + -32 + -12x

Reorder the terms:
-72 + -19x + 3x2 = 32 + -32 + 12x + -12x

Combine like terms: 32 + -32 = 0
-72 + -19x + 3x2 = 0 + 12x + -12x
-72 + -19x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-72 + -19x + 3x2 = 0

Factor a trinomial.
(-8 + -3x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2.666666667, 9}

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