Solve 3x+4x^2

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

Factor

$$x\left(4x+3\right)$$

Solution Steps

Factor out x.

$$x\left(3+4x\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$4x^{2}+3x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-3±\sqrt{3^{2}}}{2\times 4}$$

Take the square root of 3^{2}.

$$x=\frac{-3±3}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-3±3}{8}$$

Now solve the equation x=\frac{-3±3}{8} when ± is plus. Add -3 to 3.

$$x=\frac{0}{8}$$

Divide 0 by 8.

$$x=0$$

Now solve the equation x=\frac{-3±3}{8} when ± is minus. Subtract 3 from -3.

$$x=-\frac{6}{8}$$

Reduce the fraction \frac{-6}{8} to lowest terms by extracting and canceling out 2.

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

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{3}{4} for x_{2}.

$$4x^{2}+3x=4x\left(x-\left(-\frac{3}{4}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$4x^{2}+3x=4x\left(x+\frac{3}{4}\right)$$

Add \frac{3}{4} to x by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$4x^{2}+3x=4x\times \frac{4x+3}{4}$$

Cancel out 4, the greatest common factor in 4 and 4.

$$4x^{2}+3x=x\left(4x+3\right)$$

Evaluate

$$x\left(4x+3\right)$$