Question
Simplify the expression
420x4−315x3
Evaluate
(4x−3)(3x2×5x×7)
Remove the parentheses
(4x−3)×3x2×5x×7
Multiply the terms
More Steps

Evaluate
3×5×7
Multiply the terms
15×7
Multiply the numbers
105
(4x−3)×105x2×x
Multiply the terms with the same base by adding their exponents
(4x−3)×105x2+1
Add the numbers
(4x−3)×105x3
Multiply the terms
105x3(4x−3)
Apply the distributive property
105x3×4x−105x3×3
Multiply the terms
More Steps

Evaluate
105x3×4x
Multiply the numbers
420x3×x
Multiply the terms
More Steps

Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
420x4
420x4−105x3×3
Solution
420x4−315x3
Show Solution

Find the roots
x1=0,x2=43
Alternative Form
x1=0,x2=0.75
Evaluate
(4x−3)(3x2×5x×7)
To find the roots of the expression,set the expression equal to 0
(4x−3)(3x2×5x×7)=0
Multiply
More Steps

Multiply the terms
3x2×5x×7
Multiply the terms
More Steps

Evaluate
3×5×7
Multiply the terms
15×7
Multiply the numbers
105
105x2×x
Multiply the terms with the same base by adding their exponents
105x2+1
Add the numbers
105x3
(4x−3)×105x3=0
Multiply the terms
105x3(4x−3)=0
Elimination the left coefficient
x3(4x−3)=0
Separate the equation into 2 possible cases
x3=04x−3=0
The only way a power can be 0 is when the base equals 0
x=04x−3=0
Solve the equation
More Steps

Evaluate
4x−3=0
Move the constant to the right-hand side and change its sign
4x=0+3
Removing 0 doesn't change the value,so remove it from the expression
4x=3
Divide both sides
44x=43
Divide the numbers
x=43
x=0x=43
Solution
x1=0,x2=43
Alternative Form
x1=0,x2=0.75
Show Solution
