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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -2x + -16x = -18x
-21 + -18x + 3x2 = 16x + -16x

Combine like terms: 16x + -16x = 0
-21 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -6x + x2) = 0

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

Ignore the factor 3.

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 '(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, 7}

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