9x(72-x)=7x(x-40)

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Solution for 9x(72-x)=7x(x-40) equation: 


Simplifying
9x(72 + -1x) = 7x(x + -40)
(72 * 9x + -1x * 9x) = 7x(x + -40)
(648x + -9x2) = 7x(x + -40)

Reorder the terms:
648x + -9x2 = 7x(-40 + x)
648x + -9x2 = (-40 * 7x + x * 7x)
648x + -9x2 = (-280x + 7x2)

Solving
648x + -9x2 = -280x + 7x2

Solving for variable 'x'.

Reorder the terms:
648x + 280x + -9x2 + -7x2 = -280x + 7x2 + 280x + -7x2

Combine like terms: 648x + 280x = 928x
928x + -9x2 + -7x2 = -280x + 7x2 + 280x + -7x2

Combine like terms: -9x2 + -7x2 = -16x2
928x + -16x2 = -280x + 7x2 + 280x + -7x2

Reorder the terms:
928x + -16x2 = -280x + 280x + 7x2 + -7x2

Combine like terms: -280x + 280x = 0
928x + -16x2 = 0 + 7x2 + -7x2
928x + -16x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
928x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '16x'.
16x(58 + -1x) = 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 '(58 + -1x)' equal to zero and attempt to solve:

Simplifying
58 + -1x = 0

Solving
58 + -1x = 0

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

Add '-58' to each side of the equation.
58 + -58 + -1x = 0 + -58

Combine like terms: 58 + -58 = 0
0 + -1x = 0 + -58
-1x = 0 + -58

Combine like terms: 0 + -58 = -58
-1x = -58

Divide each side by '-1'.
x = 58

Simplifying
x = 58
Solution
x = {0, 58}

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