6x^2+3x-100=x^2-20x-16

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Solution for 6x^2+3x-100=x^2-20x-16 equation: 


Simplifying
6x2 + 3x + -100 = x2 + -20x + -16

Reorder the terms:
-100 + 3x + 6x2 = x2 + -20x + -16

Reorder the terms:
-100 + 3x + 6x2 = -16 + -20x + x2

Solving
-100 + 3x + 6x2 = -16 + -20x + x2

Solving for variable 'x'.

Reorder the terms:
-100 + 16 + 3x + 20x + 6x2 + -1x2 = -16 + -20x + x2 + 16 + 20x + -1x2

Combine like terms: -100 + 16 = -84
-84 + 3x + 20x + 6x2 + -1x2 = -16 + -20x + x2 + 16 + 20x + -1x2

Combine like terms: 3x + 20x = 23x
-84 + 23x + 6x2 + -1x2 = -16 + -20x + x2 + 16 + 20x + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
-84 + 23x + 5x2 = -16 + -20x + x2 + 16 + 20x + -1x2

Reorder the terms:
-84 + 23x + 5x2 = -16 + 16 + -20x + 20x + x2 + -1x2

Combine like terms: -16 + 16 = 0
-84 + 23x + 5x2 = 0 + -20x + 20x + x2 + -1x2
-84 + 23x + 5x2 = -20x + 20x + x2 + -1x2

Combine like terms: -20x + 20x = 0
-84 + 23x + 5x2 = 0 + x2 + -1x2
-84 + 23x + 5x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-84 + 23x + 5x2 = 0

Factor a trinomial.
(-7 + -1x)(12 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -5x)' equal to zero and attempt to solve:

Simplifying
12 + -5x = 0

Solving
12 + -5x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -5x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -5x = 0 + -12
-5x = 0 + -12

Combine like terms: 0 + -12 = -12
-5x = -12

Divide each side by '-5'.
x = 2.4

Simplifying
x = 2.4
Solution
x = {-7, 2.4}

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