(3x+8)(6x+7)-(2x-1)(5x-4)=0

Simple and best practice solution for (3x+8)(6x+7)-(2x-1)(5x-4)=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+8)(6x+7)-(2x-1)(5x-4)=0 equation: 


Simplifying
(3x + 8)(6x + 7) + -1(2x + -1)(5x + -4) = 0

Reorder the terms:
(8 + 3x)(6x + 7) + -1(2x + -1)(5x + -4) = 0

Reorder the terms:
(8 + 3x)(7 + 6x) + -1(2x + -1)(5x + -4) = 0

Multiply (8 + 3x) * (7 + 6x)
(8(7 + 6x) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0
((7 * 8 + 6x * 8) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0
((56 + 48x) + 3x * (7 + 6x)) + -1(2x + -1)(5x + -4) = 0
(56 + 48x + (7 * 3x + 6x * 3x)) + -1(2x + -1)(5x + -4) = 0
(56 + 48x + (21x + 18x2)) + -1(2x + -1)(5x + -4) = 0

Combine like terms: 48x + 21x = 69x
(56 + 69x + 18x2) + -1(2x + -1)(5x + -4) = 0

Reorder the terms:
56 + 69x + 18x2 + -1(-1 + 2x)(5x + -4) = 0

Reorder the terms:
56 + 69x + 18x2 + -1(-1 + 2x)(-4 + 5x) = 0

Multiply (-1 + 2x) * (-4 + 5x)
56 + 69x + 18x2 + -1(-1(-4 + 5x) + 2x * (-4 + 5x)) = 0
56 + 69x + 18x2 + -1((-4 * -1 + 5x * -1) + 2x * (-4 + 5x)) = 0
56 + 69x + 18x2 + -1((4 + -5x) + 2x * (-4 + 5x)) = 0
56 + 69x + 18x2 + -1(4 + -5x + (-4 * 2x + 5x * 2x)) = 0
56 + 69x + 18x2 + -1(4 + -5x + (-8x + 10x2)) = 0

Combine like terms: -5x + -8x = -13x
56 + 69x + 18x2 + -1(4 + -13x + 10x2) = 0
56 + 69x + 18x2 + (4 * -1 + -13x * -1 + 10x2 * -1) = 0
56 + 69x + 18x2 + (-4 + 13x + -10x2) = 0

Reorder the terms:
56 + -4 + 69x + 13x + 18x2 + -10x2 = 0

Combine like terms: 56 + -4 = 52
52 + 69x + 13x + 18x2 + -10x2 = 0

Combine like terms: 69x + 13x = 82x
52 + 82x + 18x2 + -10x2 = 0

Combine like terms: 18x2 + -10x2 = 8x2
52 + 82x + 8x2 = 0

Solving
52 + 82x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(26 + 41x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(26 + 41x + 4x2)' equal to zero and attempt to solve:

Simplifying
26 + 41x + 4x2 = 0

Solving
26 + 41x + 4x2 = 0

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

Divide each side by '4'.
6.5 + 10.25x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 10.25x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 10.25x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 10.25x + x2 = 0 + -6.5
10.25x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
10.25x + x2 = -6.5

The x term is 10.25x.  Take half its coefficient (5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
10.25x + 26.265625 + x2 = -6.5 + 26.265625

Reorder the terms:
26.265625 + 10.25x + x2 = -6.5 + 26.265625

Combine like terms: -6.5 + 26.265625 = 19.765625
26.265625 + 10.25x + x2 = 19.765625

Factor a perfect square on the left side:
(x + 5.125)(x + 5.125) = 19.765625

Calculate the square root of the right side: 4.445854811

Break this problem into two subproblems by setting 
(x + 5.125) equal to 4.445854811 and -4.445854811.


Subproblem 1
x + 5.125 = 4.445854811

Simplifying
x + 5.125 = 4.445854811

Reorder the terms:
5.125 + x = 4.445854811

Solving
5.125 + x = 4.445854811

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.125' to each side of the equation.
5.125 + -5.125 + x = 4.445854811 + -5.125

Combine like terms: 5.125 + -5.125 = 0.000
0.000 + x = 4.445854811 + -5.125
x = 4.445854811 + -5.125

Combine like terms: 4.445854811 + -5.125 = -0.679145189
x = -0.679145189

Simplifying
x = -0.679145189


Subproblem 2
x + 5.125 = -4.445854811

Simplifying
x + 5.125 = -4.445854811

Reorder the terms:
5.125 + x = -4.445854811

Solving
5.125 + x = -4.445854811

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.125' to each side of the equation.
5.125 + -5.125 + x = -4.445854811 + -5.125

Combine like terms: 5.125 + -5.125 = 0.000
0.000 + x = -4.445854811 + -5.125
x = -4.445854811 + -5.125

Combine like terms: -4.445854811 + -5.125 = -9.570854811
x = -9.570854811

Simplifying
x = -9.570854811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.679145189, -9.570854811}
Solution
x = {-0.679145189, -9.570854811}

See similar equations:

| -36b-27+37b-9=0 | | 0.23y-2.5=0.13y+2-0.8y | | Y=-.60(25)+116 | | 5.7q-1.5-5.3q=-0.6q-3.5 | | 3+5+9=72 | | 1xp=7 | | 3x+1=3x+8 | | (x)(x)(2)-7x-4=0 | | y-17=-15 | | x+1/2-3=x-1/3 | | 23y-2.5=0.13y+2-0.8y | | 2x/5-3/4=9/10 | | (3x^2-4x^2+7x-3)-(4x-2/3x^2+2)=0 | | x+3y+z=-3 | | 7t-21+t+4=15 | | 2x+z=3 | | x-y+2z=8 | | 10y+x^2=0 | | 10y=-x^2 | | 10n+14=14n-2 | | 17x/2=34/3 | | abs(4x-3)=3 | | 8*w*6=208 | | 5(2y+3)-5=-70 | | -68=2x-4(-x+5) | | 5(2y+3)-5=-7 | | 8-p=-12+3p | | 8+3(5x-2)=17 | | 3x-4(x-8)=27 | | -80=3x+4(-5x+14) | | 3x=37.5 | | 6(2x-5)+20=14 |

Equations solver categories