Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
2(x−3)(x2+3x+3)
Evaluate
2x3−12x−18
Rewrite the expression
2x3−2×6x−2×9
Factor out 2 from the expression
2(x3−6x−9)
Solution
More Steps
Evaluate
x3−6x−9
Calculate
x3+3x2+3x−3x2−9x−9
Rewrite the expression
x×x2+x×3x+x×3−3x2−3×3x−3×3
Factor out x from the expression
x(x2+3x+3)−3x2−3×3x−3×3
Factor out −3 from the expression
x(x2+3x+3)−3(x2+3x+3)
Factor out x2+3x+3 from the expression
(x−3)(x2+3x+3)
2(x−3)(x2+3x+3)
Show Solution
Find the roots
x1=−23−23i,x2=−23+23i,x3=3
Alternative Form
x1≈−1.5−0.866025i,x2≈−1.5+0.866025i,x3=3
Evaluate
2x3−12x−18
To find the roots of the expression,set the expression equal to 0
2x3−12x−18=0
Factor the expression
2(x−3)(x2+3x+3)=0
Divide both sides
(x−3)(x2+3x+3)=0
Separate the equation into 2 possible cases
x−3=0x2+3x+3=0
Solve the equation
More Steps
Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x2+3x+3=0
Solve the equation
More Steps
Evaluate
x2+3x+3=0
Substitute a=1,b=3 and c=3 into the quadratic formula x=2a−b±b2−4ac
x=2−3±32−4×3
Simplify the expression
More Steps
Evaluate
32−4×3
Multiply the numbers
32−12
Evaluate the power
9−12
Subtract the numbers
−3
x=2−3±−3
Simplify the radical expression
More Steps
Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
x=2−3±3×i
Separate the equation into 2 possible cases
x=2−3+3×ix=2−3−3×i
Simplify the expression
x=−23+23ix=2−3−3×i
Simplify the expression
x=−23+23ix=−23−23i
x=3x=−23+23ix=−23−23i
Solution
x1=−23−23i,x2=−23+23i,x3=3
Alternative Form
x1≈−1.5−0.866025i,x2≈−1.5+0.866025i,x3=3
Show Solution