Solve (2x-1)5x-(1-2x)3x^2=0

Question

Solve the equation

x_{1} = - \frac{5}{3}, x_{2} = 0, x_{3} = \frac{1}{2}

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 0, x_{3} = 0.5

Evaluate

(2 x - 1) \times 5 x - (1 - 2 x) \times 3 x^{2} = 0

Simplify

More Steps

Evaluate

(2 x - 1) \times 5 x - (1 - 2 x) \times 3 x^{2}

Multiply the first two terms

5 (2 x - 1) x - (1 - 2 x) \times 3 x^{2}

Multiply the first two terms

5 (2 x - 1) x - 3 (1 - 2 x) x^{2}

5 (2 x - 1) x - 3 (1 - 2 x) x^{2} = 0

Calculate

More Steps

Evaluate

5 (2 x - 1) x - 3 (1 - 2 x) x^{2}

Expand the expression

More Steps

Calculate

5 (2 x - 1) x

Simplify

(10 x - 5) x

Apply the distributive property

10 x \times x - 5 x

Multiply the terms

10 x^{2} - 5 x

10 x^{2} - 5 x - 3 (1 - 2 x) x^{2}

Expand the expression

More Steps

Calculate

- 3 (1 - 2 x) x^{2}

Simplify

(- 3 + 6 x) x^{2}

Apply the distributive property

- 3 x^{2} + 6 x \times x^{2}

Multiply the terms

- 3 x^{2} + 6 x^{3}

10 x^{2} - 5 x - 3 x^{2} + 6 x^{3}

Subtract the terms

More Steps

Evaluate

10 x^{2} - 3 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(10 - 3) x^{2}

Subtract the numbers

7 x^{2}

7 x^{2} - 5 x + 6 x^{3}

7 x^{2} - 5 x + 6 x^{3} = 0

Factor the expression

- x (1 - 2 x) (5 + 3 x) = 0

Separate the equation into 3 possible cases

- x = 0 1 - 2 x = 0 5 + 3 x = 0

Change the signs on both sides of the equation

x = 0 1 - 2 x = 0 5 + 3 x = 0

Solve the equation

More Steps

Evaluate

1 - 2 x = 0

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

- 2 x = 0 - 1

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

- 2 x = - 1

Change the signs on both sides of the equation

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 0 x = \frac{1}{2} 5 + 3 x = 0

Solve the equation

More Steps

Evaluate

5 + 3 x = 0

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

3 x = 0 - 5

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

3 x = - 5

Divide both sides

\frac{3 x}{3} = \frac{- 5}{3}

Divide the numbers

x = \frac{- 5}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{5}{3}

x = 0 x = \frac{1}{2} x = - \frac{5}{3}

Solution

x_{1} = - \frac{5}{3}, x_{2} = 0, x_{3} = \frac{1}{2}

Alternative Form

x_{1} = - 1. \dot{6}, x_{2} = 0, x_{3} = 0.5

Show Solution

Solve the equation

Graph