Solve -x^{2}+3x^{3}-(7+4x^2)-6x^3=-3x^3+5x^2-7

$$- x ^ { 2 } + 3 x ^ { 3 } - ( 7 + 4 x ^ { 2 } ) - 6 x ^ { 3 } = - 3 x ^ { 3 } + 5 x ^ { 2 } - 7$$

Solve for x

$$x=0$$

Steps by Finding Square Root

To find the opposite of 7+4x^{2}, find the opposite of each term.

$$-x^{2}+3x^{3}-7-4x^{2}-6x^{3}=-3x^{3}+5x^{2}-7$$

Combine 3x^{3} and -6x^{3} to get -3x^{3}.

$$-x^{2}-3x^{3}-7-4x^{2}=-3x^{3}+5x^{2}-7$$

Add 3x^{3} to both sides.

$$-x^{2}-3x^{3}-7-4x^{2}+3x^{3}=5x^{2}-7$$

Combine -3x^{3} and 3x^{3} to get 0.

$$-x^{2}-7-4x^{2}=5x^{2}-7$$

Subtract 5x^{2} from both sides.

$$-x^{2}-7-4x^{2}-5x^{2}=-7$$

Combine -4x^{2} and -5x^{2} to get -9x^{2}.

$$-x^{2}-7-9x^{2}=-7$$

Add 7 to both sides.

$$-x^{2}-9x^{2}=-7+7$$

Add -7 and 7 to get 0.

$$-x^{2}-9x^{2}=0$$

Combine -x^{2} and -9x^{2} to get -10x^{2}.

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

Divide both sides by -10. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

To find the opposite of 7+4x^{2}, find the opposite of each term.

$$-x^{2}+3x^{3}-7-4x^{2}-6x^{3}=-3x^{3}+5x^{2}-7$$

Combine 3x^{3} and -6x^{3} to get -3x^{3}.

$$-x^{2}-3x^{3}-7-4x^{2}=-3x^{3}+5x^{2}-7$$

Add 3x^{3} to both sides.

$$-x^{2}-3x^{3}-7-4x^{2}+3x^{3}=5x^{2}-7$$

Combine -3x^{3} and 3x^{3} to get 0.

$$-x^{2}-7-4x^{2}=5x^{2}-7$$

Subtract 5x^{2} from both sides.

$$-x^{2}-7-4x^{2}-5x^{2}=-7$$

Combine -4x^{2} and -5x^{2} to get -9x^{2}.

$$-x^{2}-7-9x^{2}=-7$$

Add 7 to both sides.

$$-x^{2}-7-9x^{2}+7=0$$

Add -7 and 7 to get 0.

$$-x^{2}-9x^{2}=0$$

Combine -x^{2} and -9x^{2} to get -10x^{2}.

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

Divide both sides by -10. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$