(2x-3)(x+4)=x*x+8x+16

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Solution for (2x-3)(x+4)=x*x+8x+16 equation: 


Simplifying
(2x + -3)(x + 4) = x * x + 8x + 16

Reorder the terms:
(-3 + 2x)(x + 4) = x * x + 8x + 16

Reorder the terms:
(-3 + 2x)(4 + x) = x * x + 8x + 16

Multiply (-3 + 2x) * (4 + x)
(-3(4 + x) + 2x * (4 + x)) = x * x + 8x + 16
((4 * -3 + x * -3) + 2x * (4 + x)) = x * x + 8x + 16
((-12 + -3x) + 2x * (4 + x)) = x * x + 8x + 16
(-12 + -3x + (4 * 2x + x * 2x)) = x * x + 8x + 16
(-12 + -3x + (8x + 2x2)) = x * x + 8x + 16

Combine like terms: -3x + 8x = 5x
(-12 + 5x + 2x2) = x * x + 8x + 16

Multiply x * x
-12 + 5x + 2x2 = x2 + 8x + 16

Reorder the terms:
-12 + 5x + 2x2 = 16 + 8x + x2

Solving
-12 + 5x + 2x2 = 16 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -16 + 5x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: -12 + -16 = -28
-28 + 5x + -8x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 5x + -8x = -3x
-28 + -3x + 2x2 + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-28 + -3x + 1x2 = 16 + 8x + x2 + -16 + -8x + -1x2

Reorder the terms:
-28 + -3x + 1x2 = 16 + -16 + 8x + -8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-28 + -3x + 1x2 = 0 + 8x + -8x + x2 + -1x2
-28 + -3x + 1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-28 + -3x + 1x2 = 0 + x2 + -1x2
-28 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-28 + -3x + 1x2 = 0

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


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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 = {-4, 7}

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