7x^2=-252+84x

Solution for 7x^2=-252+84x equation:

Simplifying
7x2 = -252 + 84x

Solving
7x2 = -252 + 84x

Solving for variable 'x'.

Reorder the terms:
252 + -84x + 7x2 = -252 + 84x + 252 + -84x

Reorder the terms:
252 + -84x + 7x2 = -252 + 252 + 84x + -84x

Combine like terms: -252 + 252 = 0
252 + -84x + 7x2 = 0 + 84x + -84x
252 + -84x + 7x2 = 84x + -84x

Combine like terms: 84x + -84x = 0
252 + -84x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(36 + -12x + x2) = 0

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {6, 6}