2x(x+8)-(2x-7)(2x+7)=73

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Solution for 2x(x+8)-(2x-7)(2x+7)=73 equation: 


Simplifying
2x(x + 8) + -1(2x + -7)(2x + 7) = 73

Reorder the terms:
2x(8 + x) + -1(2x + -7)(2x + 7) = 73
(8 * 2x + x * 2x) + -1(2x + -7)(2x + 7) = 73
(16x + 2x2) + -1(2x + -7)(2x + 7) = 73

Reorder the terms:
16x + 2x2 + -1(-7 + 2x)(2x + 7) = 73

Reorder the terms:
16x + 2x2 + -1(-7 + 2x)(7 + 2x) = 73

Multiply (-7 + 2x) * (7 + 2x)
16x + 2x2 + -1(-7(7 + 2x) + 2x * (7 + 2x)) = 73
16x + 2x2 + -1((7 * -7 + 2x * -7) + 2x * (7 + 2x)) = 73
16x + 2x2 + -1((-49 + -14x) + 2x * (7 + 2x)) = 73
16x + 2x2 + -1(-49 + -14x + (7 * 2x + 2x * 2x)) = 73
16x + 2x2 + -1(-49 + -14x + (14x + 4x2)) = 73

Combine like terms: -14x + 14x = 0
16x + 2x2 + -1(-49 + 0 + 4x2) = 73
16x + 2x2 + -1(-49 + 4x2) = 73
16x + 2x2 + (-49 * -1 + 4x2 * -1) = 73
16x + 2x2 + (49 + -4x2) = 73

Reorder the terms:
49 + 16x + 2x2 + -4x2 = 73

Combine like terms: 2x2 + -4x2 = -2x2
49 + 16x + -2x2 = 73

Solving
49 + 16x + -2x2 = 73

Solving for variable 'x'.

Reorder the terms:
49 + -73 + 16x + -2x2 = 73 + -73

Combine like terms: 49 + -73 = -24
-24 + 16x + -2x2 = 73 + -73

Combine like terms: 73 + -73 = 0
-24 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 8x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {6, 2}

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