(3x+5)(x-3)=12x+20

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Solution for (3x+5)(x-3)=12x+20 equation: 


Simplifying
(3x + 5)(x + -3) = 12x + 20

Reorder the terms:
(5 + 3x)(x + -3) = 12x + 20

Reorder the terms:
(5 + 3x)(-3 + x) = 12x + 20

Multiply (5 + 3x) * (-3 + x)
(5(-3 + x) + 3x * (-3 + x)) = 12x + 20
((-3 * 5 + x * 5) + 3x * (-3 + x)) = 12x + 20
((-15 + 5x) + 3x * (-3 + x)) = 12x + 20
(-15 + 5x + (-3 * 3x + x * 3x)) = 12x + 20
(-15 + 5x + (-9x + 3x2)) = 12x + 20

Combine like terms: 5x + -9x = -4x
(-15 + -4x + 3x2) = 12x + 20

Reorder the terms:
-15 + -4x + 3x2 = 20 + 12x

Solving
-15 + -4x + 3x2 = 20 + 12x

Solving for variable 'x'.

Reorder the terms:
-15 + -20 + -4x + -12x + 3x2 = 20 + 12x + -20 + -12x

Combine like terms: -15 + -20 = -35
-35 + -4x + -12x + 3x2 = 20 + 12x + -20 + -12x

Combine like terms: -4x + -12x = -16x
-35 + -16x + 3x2 = 20 + 12x + -20 + -12x

Reorder the terms:
-35 + -16x + 3x2 = 20 + -20 + 12x + -12x

Combine like terms: 20 + -20 = 0
-35 + -16x + 3x2 = 0 + 12x + -12x
-35 + -16x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-35 + -16x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1.666666667, 7}

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