Solve c^2h^6o = c^4h10o h^2o

Question

Solve the equation

Solve for c

Solve for h

Solve for o

c = 0 c = \frac{h 10 o h}{10 ∣ o ∣} c = - \frac{h 10 o h}{10 ∣ o ∣}

Evaluate

c^{2} h^{6} o = c^{4} h \times 10 o h^{2} o

Multiply

More Steps

Evaluate

c^{4} h \times 10 o h^{2} o

Multiply the terms with the same base by adding their exponents

c^{4} h^{1 + 2} \times 10 o \times o

Add the numbers

c^{4} h^{3} \times 10 o \times o

Multiply the terms

c^{4} h^{3} \times 10 o^{2}

Use the commutative property to reorder the terms

10 c^{4} h^{3} o^{2}

c^{2} h^{6} o = 10 c^{4} h^{3} o^{2}

Rewrite the expression

h^{6} o c^{2} = 10 h^{3} o^{2} c^{4}

Add or subtract both sides

h^{6} o c^{2} - 10 h^{3} o^{2} c^{4} = 0

Factor the expression

h^{3} o c^{2} (h^{3} - 10 o c^{2}) = 0

Divide both sides

c^{2} (h^{3} - 10 o c^{2}) = 0

Separate the equation into 2 possible cases

c^{2} = 0 h^{3} - 10 o c^{2} = 0

The only way a power can be 0 is when the base equals 0

c = 0 h^{3} - 10 o c^{2} = 0

Solve the equation

More Steps

Evaluate

h^{3} - 10 o c^{2} = 0

Move the expression to the right-hand side and change its sign

- 10 o c^{2} = 0 - h^{3}

Removing 0 doesn't change the value,so remove it from the expression

- 10 o c^{2} = - h^{3}

Divide both sides

\frac{- 10 o c ^{2}}{- 10 o} = \frac{- h ^{3}}{- 10 o}

Divide the numbers

c^{2} = \frac{- h ^{3}}{- 10 o}

Divide the numbers

c^{2} = \frac{h ^{3}}{10 o}

Take the root of both sides of the equation and remember to use both positive and negative roots

c = \pm \frac{h ^{3}}{10 o}

Simplify the expression

More Steps

Evaluate

\frac{h ^{3}}{10 o}

Rewrite the expression

\frac{h ^{3} \times 10 o}{10 o \times 10 o}

Use the commutative property to reorder the terms

\frac{10 h ^{3} o}{10 o \times 10 o}

Calculate

\frac{10 h ^{3} o}{100 o ^{2}}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{10 h ^{3} o}{100 o ^{2}}

Simplify the radical expression

\frac{10 h ^{3} o}{10 ∣ o ∣}

c = \pm \frac{10 h ^{3} o}{10 ∣ o ∣}

Separate the equation into 2 possible cases

c = \frac{10 h ^{3} o}{10 ∣ o ∣} c = - \frac{10 h ^{3} o}{10 ∣ o ∣}

c = 0 c = \frac{10 h ^{3} o}{10 ∣ o ∣} c = - \frac{10 h ^{3} o}{10 ∣ o ∣}

Simplify

c = 0 c = \frac{h 10 o h}{10 ∣ o ∣} c = - \frac{10 h ^{3} o}{10 ∣ o ∣}

Solution

c = 0 c = \frac{h 10 o h}{10 ∣ o ∣} c = - \frac{h 10 o h}{10 ∣ o ∣}

Show Solution