Solve 3*(2x-10).2(3x-30)=-5(3x+100)

$$3 \times (2x-10).2(3x-30)=-5(3x+100)$$

Solve for x (complex solution)

$$x=\frac{65+i\times 5\sqrt{919}}{12}\approx 5.416666667+12.631255326i$$

$$x=\frac{-i\times 5\sqrt{919}+65}{12}\approx 5.416666667-12.631255326i$$

Steps Using the Quadratic Formula

Multiply 3 and 0.2 to get 0.6.

$$0.6\left(2x-10\right)\left(3x-30\right)=-5\left(3x+100\right)$$

Use the distributive property to multiply 0.6 by 2x-10.

$$\left(1.2x-6\right)\left(3x-30\right)=-5\left(3x+100\right)$$

Use the distributive property to multiply 1.2x-6 by 3x-30 and combine like terms.

$$3.6x^{2}-54x+180=-5\left(3x+100\right)$$

Use the distributive property to multiply -5 by 3x+100.

$$3.6x^{2}-54x+180=-15x-500$$

Add 15x to both sides.

$$3.6x^{2}-54x+180+15x=-500$$

Combine -54x and 15x to get -39x.

$$3.6x^{2}-39x+180=-500$$

Add 500 to both sides.

$$3.6x^{2}-39x+180+500=0$$

Add 180 and 500 to get 680.

$$3.6x^{2}-39x+680=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3.6 for a, -39 for b, and 680 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-39\right)±\sqrt{\left(-39\right)^{2}-4\times 3.6\times 680}}{2\times 3.6}$$

Square -39.

$$x=\frac{-\left(-39\right)±\sqrt{1521-4\times 3.6\times 680}}{2\times 3.6}$$

Multiply -4 times 3.6.

$$x=\frac{-\left(-39\right)±\sqrt{1521-14.4\times 680}}{2\times 3.6}$$

Multiply -14.4 times 680.

$$x=\frac{-\left(-39\right)±\sqrt{1521-9792}}{2\times 3.6}$$

Add 1521 to -9792.

$$x=\frac{-\left(-39\right)±\sqrt{-8271}}{2\times 3.6}$$

Take the square root of -8271.

$$x=\frac{-\left(-39\right)±3\sqrt{919}i}{2\times 3.6}$$

The opposite of -39 is 39.

$$x=\frac{39±3\sqrt{919}i}{2\times 3.6}$$

Multiply 2 times 3.6.

$$x=\frac{39±3\sqrt{919}i}{7.2}$$

Now solve the equation x=\frac{39±3\sqrt{919}i}{7.2} when ± is plus. Add 39 to 3i\sqrt{919}.

$$x=\frac{39+3\sqrt{919}i}{7.2}$$

Divide 39+3i\sqrt{919} by 7.2 by multiplying 39+3i\sqrt{919} by the reciprocal of 7.2.

$$x=\frac{65+5\sqrt{919}i}{12}$$

Now solve the equation x=\frac{39±3\sqrt{919}i}{7.2} when ± is minus. Subtract 3i\sqrt{919} from 39.

$$x=\frac{-3\sqrt{919}i+39}{7.2}$$

Divide 39-3i\sqrt{919} by 7.2 by multiplying 39-3i\sqrt{919} by the reciprocal of 7.2.

$$x=\frac{-5\sqrt{919}i+65}{12}$$

The equation is now solved.

$$x=\frac{65+5\sqrt{919}i}{12} x=\frac{-5\sqrt{919}i+65}{12}$$

Steps for Completing the Square

Multiply 3 and 0.2 to get 0.6.

$$0.6\left(2x-10\right)\left(3x-30\right)=-5\left(3x+100\right)$$

Use the distributive property to multiply 0.6 by 2x-10.

$$\left(1.2x-6\right)\left(3x-30\right)=-5\left(3x+100\right)$$

Use the distributive property to multiply 1.2x-6 by 3x-30 and combine like terms.

$$3.6x^{2}-54x+180=-5\left(3x+100\right)$$

Use the distributive property to multiply -5 by 3x+100.

$$3.6x^{2}-54x+180=-15x-500$$

Add 15x to both sides.

$$3.6x^{2}-54x+180+15x=-500$$

Combine -54x and 15x to get -39x.

$$3.6x^{2}-39x+180=-500$$

Subtract 180 from both sides.

$$3.6x^{2}-39x=-500-180$$

Subtract 180 from -500 to get -680.

$$3.6x^{2}-39x=-680$$

Divide both sides of the equation by 3.6, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{3.6x^{2}-39x}{3.6}=-\frac{680}{3.6}$$

Dividing by 3.6 undoes the multiplication by 3.6.

$$x^{2}+\left(-\frac{39}{3.6}\right)x=-\frac{680}{3.6}$$

Divide -39 by 3.6 by multiplying -39 by the reciprocal of 3.6.

$$x^{2}-\frac{65}{6}x=-\frac{680}{3.6}$$

Divide -680 by 3.6 by multiplying -680 by the reciprocal of 3.6.

$$x^{2}-\frac{65}{6}x=-\frac{1700}{9}$$

Divide -\frac{65}{6}, the coefficient of the x term, by 2 to get -\frac{65}{12}. Then add the square of -\frac{65}{12} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{65}{6}x+\left(-\frac{65}{12}\right)^{2}=-\frac{1700}{9}+\left(-\frac{65}{12}\right)^{2}$$

Square -\frac{65}{12} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{65}{6}x+\frac{4225}{144}=-\frac{1700}{9}+\frac{4225}{144}$$

Add -\frac{1700}{9} to \frac{4225}{144} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{65}{6}x+\frac{4225}{144}=-\frac{22975}{144}$$

Factor x^{2}-\frac{65}{6}x+\frac{4225}{144}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{65}{12}\right)^{2}=-\frac{22975}{144}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{65}{12}\right)^{2}}=\sqrt{-\frac{22975}{144}}$$

Simplify.

$$x-\frac{65}{12}=\frac{5\sqrt{919}i}{12} x-\frac{65}{12}=-\frac{5\sqrt{919}i}{12}$$

Add \frac{65}{12} to both sides of the equation.

$$x=\frac{65+5\sqrt{919}i}{12} x=\frac{-5\sqrt{919}i+65}{12}$$