Solve -45y-63y^2

$$- 45 y - 63 y ^ { 2 }$$

Factor

$$-9y\left(7y+5\right)$$

Solution Steps

Factor out 9.

$$9\left(-5y-7y^{2}\right)$$

Consider -5y-7y^{2}. Factor out y.

$$y\left(-5-7y\right)$$

Rewrite the complete factored expression.

$$9y\left(-7y-5\right)$$

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.

$$-63y^{2}-45y=0$$

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.

$$y=\frac{-\left(-45\right)±\sqrt{\left(-45\right)^{2}}}{2\left(-63\right)}$$

Take the square root of \left(-45\right)^{2}.

$$y=\frac{-\left(-45\right)±45}{2\left(-63\right)}$$

The opposite of -45 is 45.

$$y=\frac{45±45}{2\left(-63\right)}$$

Multiply 2 times -63.

$$y=\frac{45±45}{-126}$$

Now solve the equation y=\frac{45±45}{-126} when ± is plus. Add 45 to 45.

$$y=\frac{90}{-126}$$

Reduce the fraction \frac{90}{-126} to lowest terms by extracting and canceling out 18.

$$y=-\frac{5}{7}$$

Now solve the equation y=\frac{45±45}{-126} when ± is minus. Subtract 45 from 45.

$$y=\frac{0}{-126}$$

Divide 0 by -126.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -\frac{5}{7} for x_{1} and 0 for x_{2}.

$$-63y^{2}-45y=-63\left(y-\left(-\frac{5}{7}\right)\right)y$$

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

$$-63y^{2}-45y=-63\left(y+\frac{5}{7}\right)y$$

Add \frac{5}{7} to y by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$-63y^{2}-45y=-63\times \frac{-7y-5}{-7}y$$

Cancel out 7, the greatest common factor in -63 and -7.

$$-63y^{2}-45y=9\left(-7y-5\right)y$$

Evaluate

$$-9y\left(7y+5\right)$$