x*x+7x-5=6x-3

Solution for x*x+7x-5=6x-3 equation:

Simplifying
x * x + 7x + -5 = 6x + -3

Multiply x * x
x2 + 7x + -5 = 6x + -3

Reorder the terms:
-5 + 7x + x2 = 6x + -3

Reorder the terms:
-5 + 7x + x2 = -3 + 6x

Solving
-5 + 7x + x2 = -3 + 6x

Solving for variable 'x'.

Reorder the terms:
-5 + 3 + 7x + -6x + x2 = -3 + 6x + 3 + -6x

Combine like terms: -5 + 3 = -2
-2 + 7x + -6x + x2 = -3 + 6x + 3 + -6x

Combine like terms: 7x + -6x = 1x
-2 + 1x + x2 = -3 + 6x + 3 + -6x

Reorder the terms:
-2 + 1x + x2 = -3 + 3 + 6x + -6x

Combine like terms: -3 + 3 = 0
-2 + 1x + x2 = 0 + 6x + -6x
-2 + 1x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + 1x + x2 = 0

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

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

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