(3x+4)(x-3)=12x+16

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Solution for (3x+4)(x-3)=12x+16 equation: 


Simplifying
(3x + 4)(x + -3) = 12x + 16

Reorder the terms:
(4 + 3x)(x + -3) = 12x + 16

Reorder the terms:
(4 + 3x)(-3 + x) = 12x + 16

Multiply (4 + 3x) * (-3 + x)
(4(-3 + x) + 3x * (-3 + x)) = 12x + 16
((-3 * 4 + x * 4) + 3x * (-3 + x)) = 12x + 16
((-12 + 4x) + 3x * (-3 + x)) = 12x + 16
(-12 + 4x + (-3 * 3x + x * 3x)) = 12x + 16
(-12 + 4x + (-9x + 3x2)) = 12x + 16

Combine like terms: 4x + -9x = -5x
(-12 + -5x + 3x2) = 12x + 16

Reorder the terms:
-12 + -5x + 3x2 = 16 + 12x

Solving
-12 + -5x + 3x2 = 16 + 12x

Solving for variable 'x'.

Reorder the terms:
-12 + -16 + -5x + -12x + 3x2 = 16 + 12x + -16 + -12x

Combine like terms: -12 + -16 = -28
-28 + -5x + -12x + 3x2 = 16 + 12x + -16 + -12x

Combine like terms: -5x + -12x = -17x
-28 + -17x + 3x2 = 16 + 12x + -16 + -12x

Reorder the terms:
-28 + -17x + 3x2 = 16 + -16 + 12x + -12x

Combine like terms: 16 + -16 = 0
-28 + -17x + 3x2 = 0 + 12x + -12x
-28 + -17x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-28 + -17x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 7}

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