Solve 6x^2-2x+5x-3

$$6 { x }^{ 2 } -2x+5x-3$$

Factor

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

Solution Steps

Multiply and combine like terms.

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

Factor out 3.

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

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

$$a+b=1 ab=2\left(-1\right)=-2$$

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. The only such pair is the system solution.

$$a=-1 b=2$$

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

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

Factor out x in 2x^{2}-x.

$$x\left(2x-1\right)+2x-1$$

Factor out common term 2x-1 by using distributive property.

$$\left(2x-1\right)\left(x+1\right)$$

Rewrite the complete factored expression.

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

Evaluate

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

Solution Steps

Combine -2x and 5x to get 3x.

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