10x^2-21x-42=7

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Solution for 10x^2-21x-42=7 equation: 


Simplifying
10x2 + -21x + -42 = 7

Reorder the terms:
-42 + -21x + 10x2 = 7

Solving
-42 + -21x + 10x2 = 7

Solving for variable 'x'.

Reorder the terms:
-42 + -7 + -21x + 10x2 = 7 + -7

Combine like terms: -42 + -7 = -49
-49 + -21x + 10x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-49 + -21x + 10x2 = 0

Factor a trinomial.
(-7 + -5x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve:

Simplifying
-7 + -5x = 0

Solving
-7 + -5x = 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 + -5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x = 0 + 7
-5x = 0 + 7

Combine like terms: 0 + 7 = 7
-5x = 7

Divide each side by '-5'.
x = -1.4

Simplifying
x = -1.4

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-1.4, 3.5}

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