Solve 3x(5x-1)=4x(2x+5)

$$3x(5x-1)=4x(2x+5)$$

Solve for x

$$x = \frac{23}{7} = 3\frac{2}{7} \approx 3.285714286$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 3x by 5x-1.

$$15x^{2}-3x=4x\left(2x+5\right)$$

Use the distributive property to multiply 4x by 2x+5.

$$15x^{2}-3x=8x^{2}+20x$$

Subtract 8x^{2} from both sides.

$$15x^{2}-3x-8x^{2}=20x$$

Combine 15x^{2} and -8x^{2} to get 7x^{2}.

$$7x^{2}-3x=20x$$

Subtract 20x from both sides.

$$7x^{2}-3x-20x=0$$

Combine -3x and -20x to get -23x.

$$7x^{2}-23x=0$$

Factor out x.

$$x\left(7x-23\right)=0$$

To find equation solutions, solve x=0 and 7x-23=0.

$$x=0 x=\frac{23}{7}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3x by 5x-1.

$$15x^{2}-3x=4x\left(2x+5\right)$$

Use the distributive property to multiply 4x by 2x+5.

$$15x^{2}-3x=8x^{2}+20x$$

Subtract 8x^{2} from both sides.

$$15x^{2}-3x-8x^{2}=20x$$

Combine 15x^{2} and -8x^{2} to get 7x^{2}.

$$7x^{2}-3x=20x$$

Subtract 20x from both sides.

$$7x^{2}-3x-20x=0$$

Combine -3x and -20x to get -23x.

$$7x^{2}-23x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -23 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}}}{2\times 7}$$

Take the square root of \left(-23\right)^{2}.

$$x=\frac{-\left(-23\right)±23}{2\times 7}$$

The opposite of -23 is 23.

$$x=\frac{23±23}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{23±23}{14}$$

Now solve the equation x=\frac{23±23}{14} when ± is plus. Add 23 to 23.

$$x=\frac{46}{14}$$

Reduce the fraction \frac{46}{14} to lowest terms by extracting and canceling out 2.

$$x=\frac{23}{7}$$

Now solve the equation x=\frac{23±23}{14} when ± is minus. Subtract 23 from 23.

$$x=\frac{0}{14}$$

Divide 0 by 14.

$$x=0$$

The equation is now solved.

$$x=\frac{23}{7} x=0$$

Steps for Completing the Square

Use the distributive property to multiply 3x by 5x-1.

$$15x^{2}-3x=4x\left(2x+5\right)$$

Use the distributive property to multiply 4x by 2x+5.

$$15x^{2}-3x=8x^{2}+20x$$

Subtract 8x^{2} from both sides.

$$15x^{2}-3x-8x^{2}=20x$$

Combine 15x^{2} and -8x^{2} to get 7x^{2}.

$$7x^{2}-3x=20x$$

Subtract 20x from both sides.

$$7x^{2}-3x-20x=0$$

Combine -3x and -20x to get -23x.

$$7x^{2}-23x=0$$

Divide both sides by 7.

$$\frac{7x^{2}-23x}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$x^{2}-\frac{23}{7}x=\frac{0}{7}$$

Divide 0 by 7.

$$x^{2}-\frac{23}{7}x=0$$

Divide -\frac{23}{7}, the coefficient of the x term, by 2 to get -\frac{23}{14}. Then add the square of -\frac{23}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{23}{7}x+\left(-\frac{23}{14}\right)^{2}=\left(-\frac{23}{14}\right)^{2}$$

Square -\frac{23}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{23}{7}x+\frac{529}{196}=\frac{529}{196}$$

Factor x^{2}-\frac{23}{7}x+\frac{529}{196}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{23}{14}\right)^{2}=\frac{529}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{23}{14}\right)^{2}}=\sqrt{\frac{529}{196}}$$

Simplify.

$$x-\frac{23}{14}=\frac{23}{14} x-\frac{23}{14}=-\frac{23}{14}$$

Add \frac{23}{14} to both sides of the equation.

$$x=\frac{23}{7} x=0$$