7x^2=43x+42

Solution for 7x^2=43x+42 equation:

Simplifying
7x2 = 43x + 42

Reorder the terms:
7x2 = 42 + 43x

Solving
7x2 = 42 + 43x

Solving for variable 'x'.

Reorder the terms:
-42 + -43x + 7x2 = 42 + 43x + -42 + -43x

Reorder the terms:
-42 + -43x + 7x2 = 42 + -42 + 43x + -43x

Combine like terms: 42 + -42 = 0
-42 + -43x + 7x2 = 0 + 43x + -43x
-42 + -43x + 7x2 = 43x + -43x

Combine like terms: 43x + -43x = 0
-42 + -43x + 7x2 = 0

Factor a trinomial.
(-6 + -7x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -7x)' equal to zero and attempt to solve:

Simplifying
-6 + -7x = 0

Solving
-6 + -7x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -7x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7x = 0 + 6
-7x = 0 + 6

Combine like terms: 0 + 6 = 6
-7x = 6

Divide each side by '-7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-0.8571428571, 7}