(x-4)(x+4)=(x+4)(x-7)+33

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Solution for (x-4)(x+4)=(x+4)(x-7)+33 equation: 


Simplifying
(x + -4)(x + 4) = (x + 4)(x + -7) + 33

Reorder the terms:
(-4 + x)(x + 4) = (x + 4)(x + -7) + 33

Reorder the terms:
(-4 + x)(4 + x) = (x + 4)(x + -7) + 33

Multiply (-4 + x) * (4 + x)
(-4(4 + x) + x(4 + x)) = (x + 4)(x + -7) + 33
((4 * -4 + x * -4) + x(4 + x)) = (x + 4)(x + -7) + 33
((-16 + -4x) + x(4 + x)) = (x + 4)(x + -7) + 33
(-16 + -4x + (4 * x + x * x)) = (x + 4)(x + -7) + 33
(-16 + -4x + (4x + x2)) = (x + 4)(x + -7) + 33

Combine like terms: -4x + 4x = 0
(-16 + 0 + x2) = (x + 4)(x + -7) + 33
(-16 + x2) = (x + 4)(x + -7) + 33

Reorder the terms:
-16 + x2 = (4 + x)(x + -7) + 33

Reorder the terms:
-16 + x2 = (4 + x)(-7 + x) + 33

Multiply (4 + x) * (-7 + x)
-16 + x2 = (4(-7 + x) + x(-7 + x)) + 33
-16 + x2 = ((-7 * 4 + x * 4) + x(-7 + x)) + 33
-16 + x2 = ((-28 + 4x) + x(-7 + x)) + 33
-16 + x2 = (-28 + 4x + (-7 * x + x * x)) + 33
-16 + x2 = (-28 + 4x + (-7x + x2)) + 33

Combine like terms: 4x + -7x = -3x
-16 + x2 = (-28 + -3x + x2) + 33

Reorder the terms:
-16 + x2 = -28 + 33 + -3x + x2

Combine like terms: -28 + 33 = 5
-16 + x2 = 5 + -3x + x2

Add '-1x2' to each side of the equation.
-16 + x2 + -1x2 = 5 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 + 0 = 5 + -3x + x2 + -1x2
-16 = 5 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16 = 5 + -3x + 0
-16 = 5 + -3x

Solving
-16 = 5 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-16 + 3x = 5 + -3x + 3x

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

Add '16' to each side of the equation.
-16 + 16 + 3x = 5 + 16

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

Combine like terms: 5 + 16 = 21
3x = 21

Divide each side by '3'.
x = 7

Simplifying
x = 7

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