Solve 2x-9(-2/3)+3x^2+x+4(4)+5/4

$$2 x - 9 ( - \frac { 2 } { 3 } ) + 3 x ^ { 2 } + x + 4 ( 4 ) + 5 / 4$$

Evaluate

$$3x^{2}+3x+\frac{93}{4}$$

Solution Steps

Multiply 9 and -\frac{2}{3} to get -6.

$$2x-\left(-6\right)+3x^{2}+x+4\times 4+\frac{5}{4}$$

The opposite of -6 is 6.

$$2x+6+3x^{2}+x+4\times 4+\frac{5}{4}$$

Combine 2x and x to get 3x.

$$3x+6+3x^{2}+4\times 4+\frac{5}{4}$$

Multiply 4 and 4 to get 16.

$$3x+6+3x^{2}+16+\frac{5}{4}$$

Add 6 and 16 to get 22.

$$3x+22+3x^{2}+\frac{5}{4}$$

Add 22 and \frac{5}{4} to get \frac{93}{4}.

$$3x+\frac{93}{4}+3x^{2}$$

Factor

$$\frac{3\left(4x^{2}+4x+31\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{12x+93+12x^{2}}{4}$$

Consider 8x+24+12x^{2}+4x+64+5. Multiply and combine like terms.

$$12x^{2}+12x+93$$

Consider 12x^{2}+12x+93. Factor out 3.

$$3\left(4x^{2}+4x+31\right)$$

Rewrite the complete factored expression.

$$\frac{3\left(4x^{2}+4x+31\right)}{4}$$