7x^2-8x=15

Solution for 7x^2-8x=15 equation:

Simplifying
7x2 + -8x = 15

Reorder the terms:
-8x + 7x2 = 15

Solving
-8x + 7x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + -8x + 7x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -8x + 7x2 = 0

Factor a trinomial.
(-1 + -1x)(15 + -7x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -7x)' equal to zero and attempt to solve:

Simplifying
15 + -7x = 0

Solving
15 + -7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -7x = 0 + -15
-7x = 0 + -15

Combine like terms: 0 + -15 = -15
-7x = -15

Divide each side by '-7'.
x = 2.142857143

Simplifying
x = 2.142857143
Solution
x = {-1, 2.142857143}