(4x+7)(4x-7)=16x-49

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Solution for (4x+7)(4x-7)=16x-49 equation: 


Simplifying
(4x + 7)(4x + -7) = 16x + -49

Reorder the terms:
(7 + 4x)(4x + -7) = 16x + -49

Reorder the terms:
(7 + 4x)(-7 + 4x) = 16x + -49

Multiply (7 + 4x) * (-7 + 4x)
(7(-7 + 4x) + 4x * (-7 + 4x)) = 16x + -49
((-7 * 7 + 4x * 7) + 4x * (-7 + 4x)) = 16x + -49
((-49 + 28x) + 4x * (-7 + 4x)) = 16x + -49
(-49 + 28x + (-7 * 4x + 4x * 4x)) = 16x + -49
(-49 + 28x + (-28x + 16x2)) = 16x + -49

Combine like terms: 28x + -28x = 0
(-49 + 0 + 16x2) = 16x + -49
(-49 + 16x2) = 16x + -49

Reorder the terms:
-49 + 16x2 = -49 + 16x

Add '49' to each side of the equation.
-49 + 49 + 16x2 = -49 + 49 + 16x

Combine like terms: -49 + 49 = 0
0 + 16x2 = -49 + 49 + 16x
16x2 = -49 + 49 + 16x

Combine like terms: -49 + 49 = 0
16x2 = 0 + 16x
16x2 = 16x

Solving
16x2 = 16x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '16x'.
16x(-1 + x) = 0

Ignore the factor 16.

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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