Solve 5x(6x-1)-2(12-3x^2)=25-5x

$$5 x ( 6 x - 1 ) - 2 ( 12 - 3 x ^ { 2 } ) = 25 - 5 x$$

Solve for x

$$x = -\frac{7}{6} = -1\frac{1}{6} \approx -1.166666667$$

$$x = \frac{7}{6} = 1\frac{1}{6} \approx 1.166666667$$

Steps Using Difference of Squares

Use the distributive property to multiply 5x by 6x-1.

$$30x^{2}-5x-2\left(12-3x^{2}\right)=25-5x$$

Use the distributive property to multiply -2 by 12-3x^{2}.

$$30x^{2}-5x-24+6x^{2}=25-5x$$

Combine 30x^{2} and 6x^{2} to get 36x^{2}.

$$36x^{2}-5x-24=25-5x$$

Subtract 25 from both sides.

$$36x^{2}-5x-24-25=-5x$$

Subtract 25 from -24 to get -49.

$$36x^{2}-5x-49=-5x$$

Add 5x to both sides.

$$36x^{2}-5x-49+5x=0$$

Combine -5x and 5x to get 0.

$$36x^{2}-49=0$$

Consider 36x^{2}-49. Rewrite 36x^{2}-49 as \left(6x\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(6x-7\right)\left(6x+7\right)=0$$

To find equation solutions, solve 6x-7=0 and 6x+7=0.

$$x=\frac{7}{6} x=-\frac{7}{6}$$

Steps by Finding Square Root

Use the distributive property to multiply 5x by 6x-1.

$$30x^{2}-5x-2\left(12-3x^{2}\right)=25-5x$$

Use the distributive property to multiply -2 by 12-3x^{2}.

$$30x^{2}-5x-24+6x^{2}=25-5x$$

Combine 30x^{2} and 6x^{2} to get 36x^{2}.

$$36x^{2}-5x-24=25-5x$$

Add 5x to both sides.

$$36x^{2}-5x-24+5x=25$$

Combine -5x and 5x to get 0.

$$36x^{2}-24=25$$

Add 24 to both sides.

$$36x^{2}=25+24$$

Add 25 and 24 to get 49.

$$36x^{2}=49$$

Divide both sides by 36.

$$x^{2}=\frac{49}{36}$$

Take the square root of both sides of the equation.

$$x=\frac{7}{6} x=-\frac{7}{6}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x by 6x-1.

$$30x^{2}-5x-2\left(12-3x^{2}\right)=25-5x$$

Use the distributive property to multiply -2 by 12-3x^{2}.

$$30x^{2}-5x-24+6x^{2}=25-5x$$

Combine 30x^{2} and 6x^{2} to get 36x^{2}.

$$36x^{2}-5x-24=25-5x$$

Subtract 25 from both sides.

$$36x^{2}-5x-24-25=-5x$$

Subtract 25 from -24 to get -49.

$$36x^{2}-5x-49=-5x$$

Add 5x to both sides.

$$36x^{2}-5x-49+5x=0$$

Combine -5x and 5x to get 0.

$$36x^{2}-49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and -49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 36\left(-49\right)}}{2\times 36}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 36\left(-49\right)}}{2\times 36}$$

Multiply -4 times 36.

$$x=\frac{0±\sqrt{-144\left(-49\right)}}{2\times 36}$$

Multiply -144 times -49.

$$x=\frac{0±\sqrt{7056}}{2\times 36}$$

Take the square root of 7056.

$$x=\frac{0±84}{2\times 36}$$

Multiply 2 times 36.

$$x=\frac{0±84}{72}$$

Now solve the equation x=\frac{0±84}{72} when ± is plus. Reduce the fraction \frac{84}{72} to lowest terms by extracting and canceling out 12.

$$x=\frac{7}{6}$$

Now solve the equation x=\frac{0±84}{72} when ± is minus. Reduce the fraction \frac{-84}{72} to lowest terms by extracting and canceling out 12.

$$x=-\frac{7}{6}$$

The equation is now solved.

$$x=\frac{7}{6} x=-\frac{7}{6}$$