0=-7x^2+42x+112

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Solution for 0=-7x^2+42x+112 equation: 


Simplifying
0 = -7x2 + 42x + 112

Reorder the terms:
0 = 112 + 42x + -7x2

Solving
0 = 112 + 42x + -7x2

Solving for variable 'x'.

Combine like terms: 0 + -112 = -112
-112 + -42x + 7x2 = 112 + 42x + -7x2 + -112 + -42x + 7x2

Reorder the terms:
-112 + -42x + 7x2 = 112 + -112 + 42x + -42x + -7x2 + 7x2

Combine like terms: 112 + -112 = 0
-112 + -42x + 7x2 = 0 + 42x + -42x + -7x2 + 7x2
-112 + -42x + 7x2 = 42x + -42x + -7x2 + 7x2

Combine like terms: 42x + -42x = 0
-112 + -42x + 7x2 = 0 + -7x2 + 7x2
-112 + -42x + 7x2 = -7x2 + 7x2

Combine like terms: -7x2 + 7x2 = 0
-112 + -42x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-16 + -6x + x2) = 0

Factor a trinomial.
7((-2 + -1x)(8 + -1x)) = 0

Ignore the factor 7.

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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2, 8}

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