0=2(x^2+x-72)

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Solution for 0=2(x^2+x-72) equation: 


Simplifying
0 = 2(x2 + x + -72)

Reorder the terms:
0 = 2(-72 + x + x2)
0 = (-72 * 2 + x * 2 + x2 * 2)
0 = (-144 + 2x + 2x2)

Solving
0 = -144 + 2x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 144 = 144
144 + -2x + -2x2 = -144 + 2x + 2x2 + 144 + -2x + -2x2

Reorder the terms:
144 + -2x + -2x2 = -144 + 144 + 2x + -2x + 2x2 + -2x2

Combine like terms: -144 + 144 = 0
144 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2
144 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
144 + -2x + -2x2 = 0 + 2x2 + -2x2
144 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
144 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(72 + -1x + -1x2) = 0

Factor a trinomial.
2((8 + -1x)(9 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

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

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

Simplifying
x = -9
Solution
x = {8, -9}

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