Question
Simplify the expression
4+40x−69x2
Evaluate
(2−3x)×2−(3x−2)×23x
Multiply the terms
2(2−3x)−(3x−2)×23x
Multiply the terms
2(2−3x)−23x(3x−2)
Expand the expression
More Steps

Calculate
2(2−3x)
Apply the distributive property
2×2−2×3x
Multiply the numbers
4−2×3x
Multiply the numbers
4−6x
4−6x−23x(3x−2)
Expand the expression
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Calculate
−23x(3x−2)
Apply the distributive property
−23x×3x−(−23x×2)
Multiply the terms
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Evaluate
−23x×3x
Multiply the numbers
−69x×x
Multiply the terms
−69x2
−69x2−(−23x×2)
Multiply the numbers
−69x2−(−46x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−69x2+46x
4−6x−69x2+46x
Solution
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Evaluate
−6x+46x
Collect like terms by calculating the sum or difference of their coefficients
(−6+46)x
Add the numbers
40x
4+40x−69x2
Show Solution

Factor the expression
−(2+23x)(3x−2)
Evaluate
(2−3x)×2−(3x−2)×23x
Multiply the terms
2(2−3x)−(3x−2)×23x
Multiply the terms
2(2−3x)−23x(3x−2)
Rewrite the expression
−2(3x−2)−23x(3x−2)
Factor out 3x−2 from the expression
(−2−23x)(3x−2)
Solution
−(2+23x)(3x−2)
Show Solution

Find the roots
x1=−232,x2=32
Alternative Form
x1≈−0.086957,x2=0.6˙
Evaluate
(2−3x)×2−(3x−2)(23x)
To find the roots of the expression,set the expression equal to 0
(2−3x)×2−(3x−2)(23x)=0
Multiply the terms
(2−3x)×2−(3x−2)×23x=0
Multiply the terms
2(2−3x)−(3x−2)×23x=0
Multiply the terms
2(2−3x)−23x(3x−2)=0
Calculate
More Steps

Evaluate
2(2−3x)−23x(3x−2)
Expand the expression
More Steps

Calculate
2(2−3x)
Apply the distributive property
2×2−2×3x
Multiply the numbers
4−2×3x
Multiply the numbers
4−6x
4−6x−23x(3x−2)
Expand the expression
More Steps

Calculate
−23x(3x−2)
Apply the distributive property
−23x×3x−(−23x×2)
Multiply the terms
−69x2−(−23x×2)
Multiply the numbers
−69x2−(−46x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−69x2+46x
4−6x−69x2+46x
Add the terms
More Steps

Evaluate
−6x+46x
Collect like terms by calculating the sum or difference of their coefficients
(−6+46)x
Add the numbers
40x
4+40x−69x2
4+40x−69x2=0
Factor the expression
More Steps

Evaluate
4+40x−69x2
Rewrite the expression
4+(46−6)x−69x2
Calculate
4+46x−6x−69x2
Rewrite the expression
2×2+2×23x−3x×2−3x×23x
Factor out 2 from the expression
2(2+23x)−3x×2−3x×23x
Factor out −3x from the expression
2(2+23x)−3x(2+23x)
Factor out 2+23x from the expression
(2−3x)(2+23x)
(2−3x)(2+23x)=0
When the product of factors equals 0,at least one factor is 0
2−3x=02+23x=0
Solve the equation for x
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Evaluate
2−3x=0
Move the constant to the right-hand side and change its sign
−3x=0−2
Removing 0 doesn't change the value,so remove it from the expression
−3x=−2
Change the signs on both sides of the equation
3x=2
Divide both sides
33x=32
Divide the numbers
x=32
x=322+23x=0
Solve the equation for x
More Steps

Evaluate
2+23x=0
Move the constant to the right-hand side and change its sign
23x=0−2
Removing 0 doesn't change the value,so remove it from the expression
23x=−2
Divide both sides
2323x=23−2
Divide the numbers
x=23−2
Use b−a=−ba=−ba to rewrite the fraction
x=−232
x=32x=−232
Solution
x1=−232,x2=32
Alternative Form
x1≈−0.086957,x2=0.6˙
Show Solution
