Solve 6x-3x*15x+3

$$6 x - 3 x \cdot 15 x + 3$$

Evaluate

$$3+6x-45x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$6x-3x^{2}\times 15+3$$

Multiply 3 and 15 to get 45.

$$6x-45x^{2}+3$$

Factor

$$3\left(-5x-1\right)\left(3x-1\right)$$

Solution Steps

Factor out 3.

$$3\left(2x-15xx+1\right)$$

Consider 2x-15x^{2}+1. Rearrange the polynomial to put it in standard form. Place the terms in order from highest to lowest power.

$$-15x^{2}+2x+1$$

Factor the expression by grouping. First, the expression needs to be rewritten as -15x^{2}+ax+bx+1. To find a and b, set up a system to be solved.

$$a+b=2 ab=-15=-15$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -15.

$$-1,15 -3,5$$

Calculate the sum for each pair.

$$-1+15=14 -3+5=2$$

The solution is the pair that gives sum 2.

$$a=5 b=-3$$

Rewrite -15x^{2}+2x+1 as \left(-15x^{2}+5x\right)+\left(-3x+1\right).

$$\left(-15x^{2}+5x\right)+\left(-3x+1\right)$$

Factor out -5x in the first and -1 in the second group.

$$-5x\left(3x-1\right)-\left(3x-1\right)$$

Factor out common term 3x-1 by using distributive property.

$$\left(3x-1\right)\left(-5x-1\right)$$

Rewrite the complete factored expression.

$$3\left(3x-1\right)\left(-5x-1\right)$$