Solve by Factoring 4x^2+5x-6=0

$4 x^{2} + 5 x - 6 = 0$

Step 1

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 6 = - 24$ and whose sum is $b = 5$ .

Factor $5$ out of $5 x$ .

$4 x^{2} + 5 (x) - 6 = 0$

Rewrite $5$ as $- 3$ plus $8$

$4 x^{2} + (- 3 + 8) x - 6 = 0$

Apply the distributive property.

$4 x^{2} - 3 x + 8 x - 6 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 3 x) + 8 x - 6 = 0$

Factor out the greatest common factor (GCF) from each group.

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

Factor the polynomial by factoring out the greatest common factor, $4 x - 3$ .

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

Step 2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$4 x - 3 = 0$

$x + 2 = 0$

Step 3

Set $4 x - 3$ equal to $0$ and solve for $x$ .

Set $4 x - 3$ equal to $0$ .

$4 x - 3 = 0$

Solve $4 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$4 x = 3$

Divide each term in $4 x = 3$ by $4$ and simplify.

Divide each term in $4 x = 3$ by $4$ .

$\frac{4 x}{4} = \frac{3}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{3}{4}$

Divide $x$ by $1$ .

$x = \frac{3}{4}$

Step 4

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 5

The final solution is all the values that make $(4 x - 3) (x + 2) = 0$ true.

$x = \frac{3}{4}, - 2$

Solve by Factoring 4x^2+5x-6=0

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