10x^2-17x+34=7x^2-26x+28

Solution for 10x^2-17x+34=7x^2-26x+28 equation:

Simplifying
10x2 + -17x + 34 = 7x2 + -26x + 28

Reorder the terms:
34 + -17x + 10x2 = 7x2 + -26x + 28

Reorder the terms:
34 + -17x + 10x2 = 28 + -26x + 7x2

Solving
34 + -17x + 10x2 = 28 + -26x + 7x2

Solving for variable 'x'.

Reorder the terms:
34 + -28 + -17x + 26x + 10x2 + -7x2 = 28 + -26x + 7x2 + -28 + 26x + -7x2

Combine like terms: 34 + -28 = 6
6 + -17x + 26x + 10x2 + -7x2 = 28 + -26x + 7x2 + -28 + 26x + -7x2

Combine like terms: -17x + 26x = 9x
6 + 9x + 10x2 + -7x2 = 28 + -26x + 7x2 + -28 + 26x + -7x2

Combine like terms: 10x2 + -7x2 = 3x2
6 + 9x + 3x2 = 28 + -26x + 7x2 + -28 + 26x + -7x2

Reorder the terms:
6 + 9x + 3x2 = 28 + -28 + -26x + 26x + 7x2 + -7x2

Combine like terms: 28 + -28 = 0
6 + 9x + 3x2 = 0 + -26x + 26x + 7x2 + -7x2
6 + 9x + 3x2 = -26x + 26x + 7x2 + -7x2

Combine like terms: -26x + 26x = 0
6 + 9x + 3x2 = 0 + 7x2 + -7x2
6 + 9x + 3x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
6 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 3x + x2) = 0

Factor a trinomial.
3((2 + x)(1 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-2, -1}