(3x-10)(x-20)-(2x+5)(2x+5)=0

Simple and best practice solution for (3x-10)(x-20)-(2x+5)(2x+5)=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (3x-10)(x-20)-(2x+5)(2x+5)=0 equation:


Simplifying
(3x + -10)(x + -20) + -1(2x + 5)(2x + 5) = 0

Reorder the terms:
(-10 + 3x)(x + -20) + -1(2x + 5)(2x + 5) = 0

Reorder the terms:
(-10 + 3x)(-20 + x) + -1(2x + 5)(2x + 5) = 0

Multiply (-10 + 3x) * (-20 + x)
(-10(-20 + x) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0
((-20 * -10 + x * -10) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0
((200 + -10x) + 3x * (-20 + x)) + -1(2x + 5)(2x + 5) = 0
(200 + -10x + (-20 * 3x + x * 3x)) + -1(2x + 5)(2x + 5) = 0
(200 + -10x + (-60x + 3x2)) + -1(2x + 5)(2x + 5) = 0

Combine like terms: -10x + -60x = -70x
(200 + -70x + 3x2) + -1(2x + 5)(2x + 5) = 0

Reorder the terms:
200 + -70x + 3x2 + -1(5 + 2x)(2x + 5) = 0

Reorder the terms:
200 + -70x + 3x2 + -1(5 + 2x)(5 + 2x) = 0

Multiply (5 + 2x) * (5 + 2x)
200 + -70x + 3x2 + -1(5(5 + 2x) + 2x * (5 + 2x)) = 0
200 + -70x + 3x2 + -1((5 * 5 + 2x * 5) + 2x * (5 + 2x)) = 0
200 + -70x + 3x2 + -1((25 + 10x) + 2x * (5 + 2x)) = 0
200 + -70x + 3x2 + -1(25 + 10x + (5 * 2x + 2x * 2x)) = 0
200 + -70x + 3x2 + -1(25 + 10x + (10x + 4x2)) = 0

Combine like terms: 10x + 10x = 20x
200 + -70x + 3x2 + -1(25 + 20x + 4x2) = 0
200 + -70x + 3x2 + (25 * -1 + 20x * -1 + 4x2 * -1) = 0
200 + -70x + 3x2 + (-25 + -20x + -4x2) = 0

Reorder the terms:
200 + -25 + -70x + -20x + 3x2 + -4x2 = 0

Combine like terms: 200 + -25 = 175
175 + -70x + -20x + 3x2 + -4x2 = 0

Combine like terms: -70x + -20x = -90x
175 + -90x + 3x2 + -4x2 = 0

Combine like terms: 3x2 + -4x2 = -1x2
175 + -90x + -1x2 = 0

Solving
175 + -90x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-175 + 90x + x2 = 0

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 90x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 90x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 90x + x2 = 0 + 175
90x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
90x + x2 = 175

The x term is 90x.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90x + 2025 + x2 = 175 + 2025

Reorder the terms:
2025 + 90x + x2 = 175 + 2025

Combine like terms: 175 + 2025 = 2200
2025 + 90x + x2 = 2200

Factor a perfect square on the left side:
(x + 45)(x + 45) = 2200

Calculate the square root of the right side: 46.904157598

Break this problem into two subproblems by setting 
(x + 45) equal to 46.904157598 and -46.904157598.

Subproblem 1

x + 45 = 46.904157598 Simplifying x + 45 = 46.904157598 Reorder the terms: 45 + x = 46.904157598 Solving 45 + x = 46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 46.904157598 + -45 Combine like terms: 45 + -45 = 0 0 + x = 46.904157598 + -45 x = 46.904157598 + -45 Combine like terms: 46.904157598 + -45 = 1.904157598 x = 1.904157598 Simplifying x = 1.904157598

Subproblem 2

x + 45 = -46.904157598 Simplifying x + 45 = -46.904157598 Reorder the terms: 45 + x = -46.904157598 Solving 45 + x = -46.904157598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -46.904157598 + -45 Combine like terms: 45 + -45 = 0 0 + x = -46.904157598 + -45 x = -46.904157598 + -45 Combine like terms: -46.904157598 + -45 = -91.904157598 x = -91.904157598 Simplifying x = -91.904157598

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.904157598, -91.904157598}

See similar equations:

| 3(6x+2)=24 | | 0=16t^2+27t-10 | | 4f+9k=2 | | 5r=55 | | 2(u-8)=-2u+24 | | -2R=48 | | x+8=-3x-4 | | z+40+z+35=6z+6 | | x+4*3=x*2+7 | | 70+65+x+53=180 | | 1n+1=1 | | A=.5h*a+b | | -2(5k-2)=34 | | 2s+49+49=9s | | -2(-2+3x)=58 | | -21=-7M | | 5d(4)d=-2 | | 100-4h=140-12h | | 2.1y=63 | | 3(9+5x)=147 | | c+21+c+7=5c-44 | | .83c-.66c=.33 | | -26m=-546 | | z-(z+-6)-2=-10 | | 8y-2+y=-31 | | 2c+45=c | | 4(-7x+7)=28 | | -9u+6=-3(u+8) | | -2(96)= | | y=-x/2-4 | | 4c+3+c+9=7c-40 | | 12-1/6m=16 |

Equations solver categories