0=(100-x)*(30+4x)

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Solution for 0=(100-x)*(30+4x) equation: 


Simplifying
0 = (100 + -1x)(30 + 4x)

Multiply (100 + -1x) * (30 + 4x)
0 = (100(30 + 4x) + -1x * (30 + 4x))
0 = ((30 * 100 + 4x * 100) + -1x * (30 + 4x))
0 = ((3000 + 400x) + -1x * (30 + 4x))
0 = (3000 + 400x + (30 * -1x + 4x * -1x))
0 = (3000 + 400x + (-30x + -4x2))

Combine like terms: 400x + -30x = 370x
0 = (3000 + 370x + -4x2)

Solving
0 = 3000 + 370x + -4x2

Solving for variable 'x'.

Combine like terms: 0 + -3000 = -3000
-3000 + -370x + 4x2 = 3000 + 370x + -4x2 + -3000 + -370x + 4x2

Reorder the terms:
-3000 + -370x + 4x2 = 3000 + -3000 + 370x + -370x + -4x2 + 4x2

Combine like terms: 3000 + -3000 = 0
-3000 + -370x + 4x2 = 0 + 370x + -370x + -4x2 + 4x2
-3000 + -370x + 4x2 = 370x + -370x + -4x2 + 4x2

Combine like terms: 370x + -370x = 0
-3000 + -370x + 4x2 = 0 + -4x2 + 4x2
-3000 + -370x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-3000 + -370x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1500 + -185x + 2x2) = 0

Factor a trinomial.
2((-15 + -2x)(100 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -2x)' equal to zero and attempt to solve:

Simplifying
-15 + -2x = 0

Solving
-15 + -2x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -2x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2x = 0 + 15
-2x = 0 + 15

Combine like terms: 0 + 15 = 15
-2x = 15

Divide each side by '-2'.
x = -7.5

Simplifying
x = -7.5

Subproblem 2
Set the factor '(100 + -1x)' equal to zero and attempt to solve:

Simplifying
100 + -1x = 0

Solving
100 + -1x = 0

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

Add '-100' to each side of the equation.
100 + -100 + -1x = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -1x = 0 + -100
-1x = 0 + -100

Combine like terms: 0 + -100 = -100
-1x = -100

Divide each side by '-1'.
x = 100

Simplifying
x = 100
Solution
x = {-7.5, 100}

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