Solve 2x(7x-3)=4x

$$2 x ( 7 x - 3 ) = 4 x$$

Solve for x

$$x=\frac{5}{7}\approx 0.714285714$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 2x by 7x-3.

$$14x^{2}-6x=4x$$

Subtract 4x from both sides.

$$14x^{2}-6x-4x=0$$

Combine -6x and -4x to get -10x.

$$14x^{2}-10x=0$$

Factor out x.

$$x\left(14x-10\right)=0$$

To find equation solutions, solve x=0 and 14x-10=0.

$$x=0 x=\frac{5}{7}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by 7x-3.

$$14x^{2}-6x=4x$$

Subtract 4x from both sides.

$$14x^{2}-6x-4x=0$$

Combine -6x and -4x to get -10x.

$$14x^{2}-10x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 14 for a, -10 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 14}$$

Take the square root of \left(-10\right)^{2}.

$$x=\frac{-\left(-10\right)±10}{2\times 14}$$

The opposite of -10 is 10.

$$x=\frac{10±10}{2\times 14}$$

Multiply 2 times 14.

$$x=\frac{10±10}{28}$$

Now solve the equation x=\frac{10±10}{28} when ± is plus. Add 10 to 10.

$$x=\frac{20}{28}$$

Reduce the fraction \frac{20}{28} to lowest terms by extracting and canceling out 4.

$$x=\frac{5}{7}$$

Now solve the equation x=\frac{10±10}{28} when ± is minus. Subtract 10 from 10.

$$x=\frac{0}{28}$$

Divide 0 by 28.

$$x=0$$

The equation is now solved.

$$x=\frac{5}{7} x=0$$

Steps for Completing the Square

Use the distributive property to multiply 2x by 7x-3.

$$14x^{2}-6x=4x$$

Subtract 4x from both sides.

$$14x^{2}-6x-4x=0$$

Combine -6x and -4x to get -10x.

$$14x^{2}-10x=0$$

Divide both sides by 14.

$$\frac{14x^{2}-10x}{14}=\frac{0}{14}$$

Dividing by 14 undoes the multiplication by 14.

$$x^{2}+\left(-\frac{10}{14}\right)x=\frac{0}{14}$$

Reduce the fraction \frac{-10}{14} to lowest terms by extracting and canceling out 2.

$$x^{2}-\frac{5}{7}x=\frac{0}{14}$$

Divide 0 by 14.

$$x^{2}-\frac{5}{7}x=0$$

Divide -\frac{5}{7}, the coefficient of the x term, by 2 to get -\frac{5}{14}. Then add the square of -\frac{5}{14} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{5}{7}x+\left(-\frac{5}{14}\right)^{2}=\left(-\frac{5}{14}\right)^{2}$$

Square -\frac{5}{14} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{5}{7}x+\frac{25}{196}=\frac{25}{196}$$

Factor x^{2}-\frac{5}{7}x+\frac{25}{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}.

$$\left(x-\frac{5}{14}\right)^{2}=\frac{25}{196}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{5}{14}\right)^{2}}=\sqrt{\frac{25}{196}}$$

Simplify.

$$x-\frac{5}{14}=\frac{5}{14} x-\frac{5}{14}=-\frac{5}{14}$$

Add \frac{5}{14} to both sides of the equation.

$$x=\frac{5}{7} x=0$$