0=4x^2-340x+3000

Solution for 0=4x^2-340x+3000 equation:

Simplifying
0 = 4x2 + -340x + 3000

Reorder the terms:
0 = 3000 + -340x + 4x2

Solving
0 = 3000 + -340x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -3000 = -3000
-3000 + 340x + -4x2 = 3000 + -340x + 4x2 + -3000 + 340x + -4x2

Reorder the terms:
-3000 + 340x + -4x2 = 3000 + -3000 + -340x + 340x + 4x2 + -4x2

Combine like terms: 3000 + -3000 = 0
-3000 + 340x + -4x2 = 0 + -340x + 340x + 4x2 + -4x2
-3000 + 340x + -4x2 = -340x + 340x + 4x2 + -4x2

Combine like terms: -340x + 340x = 0
-3000 + 340x + -4x2 = 0 + 4x2 + -4x2
-3000 + 340x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3000 + 340x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-750 + 85x + -1x2) = 0

Factor a trinomial.
4((-75 + x)(10 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-75 + x)' equal to zero and attempt to solve:

Simplifying
-75 + x = 0

Solving
-75 + x = 0

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

Add '75' to each side of the equation.
-75 + 75 + x = 0 + 75

Combine like terms: -75 + 75 = 0
0 + x = 0 + 75
x = 0 + 75

Combine like terms: 0 + 75 = 75
x = 75

Simplifying
x = 75
Subproblem 2
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
Solution
x = {75, 10}