Algebra Examples

$(m + 4) (4 m - 2) = 5 (m + 3) - 10$

Step 1

Move all terms to the left side of the equation and simplify.

Tap for more steps...

Step 1.1

Simplify the left side.

Tap for more steps...

Step 1.1.1

Simplify $(m + 4) (4 m - 2)$ .

Tap for more steps...

Step 1.1.1.1

Expand $(m + 4) (4 m - 2)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1.1.1

Apply the distributive property.

$m (4 m - 2) + 4 (4 m - 2) = 5 (m + 3) - 10$

Step 1.1.1.1.2

Apply the distributive property.

$m (4 m) + m \cdot - 2 + 4 (4 m - 2) = 5 (m + 3) - 10$

Step 1.1.1.1.3

Apply the distributive property.

$m (4 m) + m \cdot - 2 + 4 (4 m) + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.1.1.2.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.1.1

Rewrite using the commutative property of multiplication.

$4 m \cdot m + m \cdot - 2 + 4 (4 m) + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2.1.2

Multiply $m$ by $m$ by adding the exponents.

Tap for more steps...

Step 1.1.1.2.1.2.1

Move $m$ .

$4 (m \cdot m) + m \cdot - 2 + 4 (4 m) + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2.1.2.2

Multiply $m$ by $m$ .

$4 m^{2} + m \cdot - 2 + 4 (4 m) + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2.1.3

Move $- 2$ to the left of $m$ .

$4 m^{2} - 2 \cdot m + 4 (4 m) + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2.1.4

Multiply $4$ by $4$ .

$4 m^{2} - 2 m + 16 m + 4 \cdot - 2 = 5 (m + 3) - 10$

Step 1.1.1.2.1.5

Multiply $4$ by $- 2$ .

$4 m^{2} - 2 m + 16 m - 8 = 5 (m + 3) - 10$

Step 1.1.1.2.2

Add $- 2 m$ and $16 m$ .

$4 m^{2} + 14 m - 8 = 5 (m + 3) - 10$

Step 1.2

Simplify the right side.

Tap for more steps...

Step 1.2.1

Simplify $5 (m + 3) - 10$ .

Tap for more steps...

Step 1.2.1.1

Simplify each term.

Tap for more steps...

Step 1.2.1.1.1

Apply the distributive property.

$4 m^{2} + 14 m - 8 = 5 m + 5 \cdot 3 - 10$

Step 1.2.1.1.2

Multiply $5$ by $3$ .

$4 m^{2} + 14 m - 8 = 5 m + 15 - 10$

Step 1.2.1.2

Subtract $10$ from $15$ .

$4 m^{2} + 14 m - 8 = 5 m + 5$

Step 1.3

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.3.1

Subtract $5 m$ from both sides of the equation.

$4 m^{2} + 14 m - 8 - 5 m = 5$

Step 1.3.2

Subtract $5$ from both sides of the equation.

$4 m^{2} + 14 m - 8 - 5 m - 5 = 0$

Step 1.4

Simplify $4 m^{2} + 14 m - 8 - 5 m - 5$ .

Tap for more steps...

Step 1.4.1

Subtract $5 m$ from $14 m$ .

$4 m^{2} + 9 m - 8 - 5 = 0$

Step 1.4.2

Subtract $5$ from $- 8$ .

$4 m^{2} + 9 m - 13 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 4$ , $b = 9$ , and $c = - 13$ into the quadratic formula and solve for $m$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (4 \cdot - 13)}}{2 \cdot 4}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $9$ to the power of $2$ .

$m = \frac{- 9 \pm \sqrt{81 - 4 \cdot 4 \cdot - 13}}{2 \cdot 4}$

Step 4.1.2

Multiply $- 4 \cdot 4 \cdot - 13$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $4$ .

$m = \frac{- 9 \pm \sqrt{81 - 16 \cdot - 13}}{2 \cdot 4}$

Step 4.1.2.2

Multiply $- 16$ by $- 13$ .

$m = \frac{- 9 \pm \sqrt{81 + 208}}{2 \cdot 4}$

Step 4.1.3

Add $81$ and $208$ .

$m = \frac{- 9 \pm \sqrt{289}}{2 \cdot 4}$

Step 4.1.4

Rewrite $289$ as $17^{2}$ .

$m = \frac{- 9 \pm \sqrt{17^{2}}}{2 \cdot 4}$

Step 4.1.5

Pull terms out from under the radical, assuming positive real numbers.

$m = \frac{- 9 \pm 17}{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$m = \frac{- 9 \pm 17}{8}$

Step 5

The final answer is the combination of both solutions.

$m = 1, - \frac{13}{4}$