Solve x(4x-2)+x(3x+7)

Question

Simplify the expression

Solution

7 x^{2} + 5 x

Evaluate

x (4 x - 2) + x (3 x + 7)

Expand the expression

More Steps

Calculate

x (4 x - 2)

Apply the distributive property

x \times 4 x - x \times 2

Multiply the terms

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Evaluate

x \times 4 x

Use the commutative property to reorder the terms

4 x \times x

Multiply the terms

4 x^{2}

4 x^{2} - x \times 2

Use the commutative property to reorder the terms

4 x^{2} - 2 x

4 x^{2} - 2 x + x (3 x + 7)

Expand the expression

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Calculate

x (3 x + 7)

Apply the distributive property

x \times 3 x + x \times 7

Multiply the terms

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Evaluate

x \times 3 x

Use the commutative property to reorder the terms

3 x \times x

Multiply the terms

3 x^{2}

3 x^{2} + x \times 7

Use the commutative property to reorder the terms

3 x^{2} + 7 x

4 x^{2} - 2 x + 3 x^{2} + 7 x

Add the terms

More Steps

Evaluate

4 x^{2} + 3 x^{2}

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

(4 + 3) x^{2}

Add the numbers

7 x^{2}

7 x^{2} - 2 x + 7 x

Solution

More Steps

Evaluate

- 2 x + 7 x

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

(- 2 + 7) x

Add the numbers

5 x

7 x^{2} + 5 x

Show Solution

Factor the expression

Factor

x (7 x + 5)

Evaluate

x (4 x - 2) + x (3 x + 7)

Factor out x from the expression

x (4 x - 2 + 3 x + 7)

Solution

x (7 x + 5)

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{5}{7}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{7} 1428 \dot{5}, x_{2} = 0

Evaluate

x (4 x - 2) + x (3 x + 7)

To find the roots of the expression,set the expression equal to 0

x (4 x - 2) + x (3 x + 7) = 0

Calculate

More Steps

Evaluate

x (4 x - 2) + x (3 x + 7)

Expand the expression

More Steps

Calculate

x (4 x - 2)

Apply the distributive property

x \times 4 x - x \times 2

Multiply the terms

4 x^{2} - x \times 2

Use the commutative property to reorder the terms

4 x^{2} - 2 x

4 x^{2} - 2 x + x (3 x + 7)

Expand the expression

More Steps

Calculate

x (3 x + 7)

Apply the distributive property

x \times 3 x + x \times 7

Multiply the terms

3 x^{2} + x \times 7

Use the commutative property to reorder the terms

3 x^{2} + 7 x

4 x^{2} - 2 x + 3 x^{2} + 7 x

Add the terms

More Steps

Evaluate

4 x^{2} + 3 x^{2}

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

(4 + 3) x^{2}

Add the numbers

7 x^{2}

7 x^{2} - 2 x + 7 x

Add the terms

More Steps

Evaluate

- 2 x + 7 x

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

(- 2 + 7) x

Add the numbers

5 x

7 x^{2} + 5 x

7 x^{2} + 5 x = 0

Factor the expression

More Steps

Evaluate

7 x^{2} + 5 x

Rewrite the expression

x \times 7 x + x \times 5

Factor out x from the expression

x (7 x + 5)

x (7 x + 5) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 7 x + 5 = 0

Solve the equation for x

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Evaluate

7 x + 5 = 0

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

7 x = 0 - 5

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

7 x = - 5

Divide both sides

\frac{7 x}{7} = \frac{- 5}{7}

Divide the numbers

x = \frac{- 5}{7}

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

x = - \frac{5}{7}

x = 0 x = - \frac{5}{7}

Solution

x_{1} = - \frac{5}{7}, x_{2} = 0

Alternative Form

x_{1} = - 0. \dot{7} 1428 \dot{5}, x_{2} = 0

Show Solution

X(4x 2)+x(3x+7)

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression