(3x+7)(x-3)=-16

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Solution for (3x+7)(x-3)=-16 equation: 


Simplifying
(3x + 7)(x + -3) = -16

Reorder the terms:
(7 + 3x)(x + -3) = -16

Reorder the terms:
(7 + 3x)(-3 + x) = -16

Multiply (7 + 3x) * (-3 + x)
(7(-3 + x) + 3x * (-3 + x)) = -16
((-3 * 7 + x * 7) + 3x * (-3 + x)) = -16
((-21 + 7x) + 3x * (-3 + x)) = -16
(-21 + 7x + (-3 * 3x + x * 3x)) = -16
(-21 + 7x + (-9x + 3x2)) = -16

Combine like terms: 7x + -9x = -2x
(-21 + -2x + 3x2) = -16

Solving
-21 + -2x + 3x2 = -16

Solving for variable 'x'.

Reorder the terms:
-21 + 16 + -2x + 3x2 = -16 + 16

Combine like terms: -21 + 16 = -5
-5 + -2x + 3x2 = -16 + 16

Combine like terms: -16 + 16 = 0
-5 + -2x + 3x2 = 0

Factor a trinomial.
(-1 + -1x)(5 + -3x) = 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 '(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
Solution
x = {-1, 1.666666667}

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