7500=-30x^2+800x+2500

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Solution for 7500=-30x^2+800x+2500 equation: 


Simplifying
7500 = -30x2 + 800x + 2500

Reorder the terms:
7500 = 2500 + 800x + -30x2

Solving
7500 = 2500 + 800x + -30x2

Solving for variable 'x'.

Combine like terms: 7500 + -2500 = 5000
5000 + -800x + 30x2 = 2500 + 800x + -30x2 + -2500 + -800x + 30x2

Reorder the terms:
5000 + -800x + 30x2 = 2500 + -2500 + 800x + -800x + -30x2 + 30x2

Combine like terms: 2500 + -2500 = 0
5000 + -800x + 30x2 = 0 + 800x + -800x + -30x2 + 30x2
5000 + -800x + 30x2 = 800x + -800x + -30x2 + 30x2

Combine like terms: 800x + -800x = 0
5000 + -800x + 30x2 = 0 + -30x2 + 30x2
5000 + -800x + 30x2 = -30x2 + 30x2

Combine like terms: -30x2 + 30x2 = 0
5000 + -800x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(500 + -80x + 3x2) = 0

Factor a trinomial.
10((10 + -1x)(50 + -3x)) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(50 + -3x)' equal to zero and attempt to solve:

Simplifying
50 + -3x = 0

Solving
50 + -3x = 0

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

Add '-50' to each side of the equation.
50 + -50 + -3x = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -3x = 0 + -50
-3x = 0 + -50

Combine like terms: 0 + -50 = -50
-3x = -50

Divide each side by '-3'.
x = 16.66666667

Simplifying
x = 16.66666667
Solution
x = {10, 16.66666667}

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