(10x+7)(7x+3)=180

Simple and best practice solution for (10x+7)(7x+3)=180 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 (10x+7)(7x+3)=180 equation:


Simplifying
(10x + 7)(7x + 3) = 180

Reorder the terms:
(7 + 10x)(7x + 3) = 180

Reorder the terms:
(7 + 10x)(3 + 7x) = 180

Multiply (7 + 10x) * (3 + 7x)
(7(3 + 7x) + 10x * (3 + 7x)) = 180
((3 * 7 + 7x * 7) + 10x * (3 + 7x)) = 180
((21 + 49x) + 10x * (3 + 7x)) = 180
(21 + 49x + (3 * 10x + 7x * 10x)) = 180
(21 + 49x + (30x + 70x2)) = 180

Combine like terms: 49x + 30x = 79x
(21 + 79x + 70x2) = 180

Solving
21 + 79x + 70x2 = 180

Solving for variable 'x'.

Reorder the terms:
21 + -180 + 79x + 70x2 = 180 + -180

Combine like terms: 21 + -180 = -159
-159 + 79x + 70x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-159 + 79x + 70x2 = 0

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

Divide each side by '70'.
-2.271428571 + 1.128571429x + x2 = 0.0

Move the constant term to the right:

Add '2.271428571' to each side of the equation.
-2.271428571 + 1.128571429x + 2.271428571 + x2 = 0.0 + 2.271428571

Reorder the terms:
-2.271428571 + 2.271428571 + 1.128571429x + x2 = 0.0 + 2.271428571

Combine like terms: -2.271428571 + 2.271428571 = 0.000000000
0.000000000 + 1.128571429x + x2 = 0.0 + 2.271428571
1.128571429x + x2 = 0.0 + 2.271428571

Combine like terms: 0.0 + 2.271428571 = 2.271428571
1.128571429x + x2 = 2.271428571

The x term is 1.128571429x.  Take half its coefficient (0.5642857145).
Square it (0.3184183676) and add it to both sides.

Add '0.3184183676' to each side of the equation.
1.128571429x + 0.3184183676 + x2 = 2.271428571 + 0.3184183676

Reorder the terms:
0.3184183676 + 1.128571429x + x2 = 2.271428571 + 0.3184183676

Combine like terms: 2.271428571 + 0.3184183676 = 2.5898469386
0.3184183676 + 1.128571429x + x2 = 2.5898469386

Factor a perfect square on the left side:
(x + 0.5642857145)(x + 0.5642857145) = 2.5898469386

Calculate the square root of the right side: 1.609300139

Break this problem into two subproblems by setting 
(x + 0.5642857145) equal to 1.609300139 and -1.609300139.

Subproblem 1

x + 0.5642857145 = 1.609300139 Simplifying x + 0.5642857145 = 1.609300139 Reorder the terms: 0.5642857145 + x = 1.609300139 Solving 0.5642857145 + x = 1.609300139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5642857145' to each side of the equation. 0.5642857145 + -0.5642857145 + x = 1.609300139 + -0.5642857145 Combine like terms: 0.5642857145 + -0.5642857145 = 0.0000000000 0.0000000000 + x = 1.609300139 + -0.5642857145 x = 1.609300139 + -0.5642857145 Combine like terms: 1.609300139 + -0.5642857145 = 1.0450144245 x = 1.0450144245 Simplifying x = 1.0450144245

Subproblem 2

x + 0.5642857145 = -1.609300139 Simplifying x + 0.5642857145 = -1.609300139 Reorder the terms: 0.5642857145 + x = -1.609300139 Solving 0.5642857145 + x = -1.609300139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5642857145' to each side of the equation. 0.5642857145 + -0.5642857145 + x = -1.609300139 + -0.5642857145 Combine like terms: 0.5642857145 + -0.5642857145 = 0.0000000000 0.0000000000 + x = -1.609300139 + -0.5642857145 x = -1.609300139 + -0.5642857145 Combine like terms: -1.609300139 + -0.5642857145 = -2.1735858535 x = -2.1735858535 Simplifying x = -2.1735858535

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.0450144245, -2.1735858535}

See similar equations:

| 6x^2-7x=4 | | 4y-(4-y)=-20 | | 9-p=2p | | 4(5a-8)+2=12a+6 | | 1/7x-6=3/7x+4 | | 50-10P=20+10P | | 8x+6=110 | | x^2-8x+16=26 | | -7x+7(4x-14)=112 | | 18t^2-48t-32=0 | | 8(x-15)=-4(x+8) | | 8x+3=-7+5x+25 | | 10+4x-3x=22 | | -v+5+6v=1+5v+8 | | 3w+11=-2 | | 60000-500P=20000 | | -5(7x-8)=-30 | | Y+-7y+6=30 | | 8x+y-9x+3z+2x-7y+z= | | 0.90x+0.10x= | | y-7y=-2+8 | | -5(n+1)+7n=-3(3n-2) | | 0.90x+0.10= | | 60000-5P=500P | | 11h+16=70 | | log(5)*(x+1)+log(5)*(2x+1)=4 | | 100+25x=35x+75 | | 3(6x+4)=-96 | | -2y-6=-2x | | 8y=-5 | | 3(3x+4)-2=2(2x+5)-x | | 9-6x=-45 |

Equations solver categories