(3x+4)(3x-4)=9x-16

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Solution for (3x+4)(3x-4)=9x-16 equation: 


Simplifying
(3x + 4)(3x + -4) = 9x + -16

Reorder the terms:
(4 + 3x)(3x + -4) = 9x + -16

Reorder the terms:
(4 + 3x)(-4 + 3x) = 9x + -16

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

Combine like terms: 12x + -12x = 0
(-16 + 0 + 9x2) = 9x + -16
(-16 + 9x2) = 9x + -16

Reorder the terms:
-16 + 9x2 = -16 + 9x

Add '16' to each side of the equation.
-16 + 16 + 9x2 = -16 + 16 + 9x

Combine like terms: -16 + 16 = 0
0 + 9x2 = -16 + 16 + 9x
9x2 = -16 + 16 + 9x

Combine like terms: -16 + 16 = 0
9x2 = 0 + 9x
9x2 = 9x

Solving
9x2 = 9x

Solving for variable 'x'.

Reorder the terms:
-9x + 9x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-1 + x) = 0

Ignore the factor 9.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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