3×2+7x-24=13x

Subtract 13x from both sides of the equation.

3×2+7x-24-13x=0

Subtract 13x from 7x.

3×2-6x-24=0

3×2-6x-24=0

Factor 3 out of 3×2-6x-24.

Factor 3 out of 3×2.

3(x2)-6x-24=0

Factor 3 out of -6x.

3(x2)+3(-2x)-24=0

Factor 3 out of -24.

3×2+3(-2x)+3⋅-8=0

Factor 3 out of 3×2+3(-2x).

3(x2-2x)+3⋅-8=0

Factor 3 out of 3(x2-2x)+3⋅-8.

3(x2-2x-8)=0

3(x2-2x-8)=0

Factor.

Factor x2-2x-8 using the AC method.

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -8 and whose sum is -2.

-4,2

Write the factored form using these integers.

3((x-4)(x+2))=0

3((x-4)(x+2))=0

Remove unnecessary parentheses.

3(x-4)(x+2)=0

3(x-4)(x+2)=0

3(x-4)(x+2)=0

Divide each term in 3(x-4)(x+2)=0 by 3.

3(x-4)(x+2)3=03

Simplify 3(x-4)(x+2)3.

Cancel the common factor of 3.

Cancel the common factor.

3(x-4)(x+2)3=03

Divide (x-4)(x+2) by 1.

(x-4)(x+2)=03

(x-4)(x+2)=03

Expand (x-4)(x+2) using the FOIL Method.

Apply the distributive property.

x(x+2)-4(x+2)=03

Apply the distributive property.

x⋅x+x⋅2-4(x+2)=03

Apply the distributive property.

x⋅x+x⋅2-4x-4⋅2=03

x⋅x+x⋅2-4x-4⋅2=03

Simplify and combine like terms.

Simplify each term.

Multiply x by x.

x2+x⋅2-4x-4⋅2=03

Move 2 to the left of x.

x2+2⋅x-4x-4⋅2=03

Multiply -4 by 2.

x2+2x-4x-8=03

x2+2x-4x-8=03

Subtract 4x from 2x.

x2-2x-8=03

x2-2x-8=03

x2-2x-8=03

Divide 0 by 3.

x2-2x-8=0

x2-2x-8=0

Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -8 and whose sum is -2.

-4,2

Write the factored form using these integers.

(x-4)(x+2)=0

(x-4)(x+2)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x-4=0

x+2=0

Set the first factor equal to 0.

x-4=0

Add 4 to both sides of the equation.

x=4

x=4

Set the next factor equal to 0.

x+2=0

Subtract 2 from both sides of the equation.

x=-2

x=-2

The final solution is all the values that make (x-4)(x+2)=0 true.

x=4,-2

Solve using the Square Root Property 3x^2+7x-24=13x