(54-x)(150+4x)=8100

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Solution for (54-x)(150+4x)=8100 equation: 


Simplifying
(54 + -1x)(150 + 4x) = 8100

Multiply (54 + -1x) * (150 + 4x)
(54(150 + 4x) + -1x * (150 + 4x)) = 8100
((150 * 54 + 4x * 54) + -1x * (150 + 4x)) = 8100
((8100 + 216x) + -1x * (150 + 4x)) = 8100
(8100 + 216x + (150 * -1x + 4x * -1x)) = 8100
(8100 + 216x + (-150x + -4x2)) = 8100

Combine like terms: 216x + -150x = 66x
(8100 + 66x + -4x2) = 8100

Add '-8100' to each side of the equation.
8100 + 66x + -8100 + -4x2 = 8100 + -8100

Reorder the terms:
8100 + -8100 + 66x + -4x2 = 8100 + -8100

Combine like terms: 8100 + -8100 = 0
0 + 66x + -4x2 = 8100 + -8100
66x + -4x2 = 8100 + -8100

Combine like terms: 8100 + -8100 = 0
66x + -4x2 = 0

Solving
66x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(33 + -2x) = 0

Ignore the factor 2.

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 '(33 + -2x)' equal to zero and attempt to solve:

Simplifying
33 + -2x = 0

Solving
33 + -2x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -2x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -2x = 0 + -33
-2x = 0 + -33

Combine like terms: 0 + -33 = -33
-2x = -33

Divide each side by '-2'.
x = 16.5

Simplifying
x = 16.5
Solution
x = {0, 16.5}

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