5x^2-20x-21=3x^2-11x+14

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Solution for 5x^2-20x-21=3x^2-11x+14 equation: 


Simplifying
5x2 + -20x + -21 = 3x2 + -11x + 14

Reorder the terms:
-21 + -20x + 5x2 = 3x2 + -11x + 14

Reorder the terms:
-21 + -20x + 5x2 = 14 + -11x + 3x2

Solving
-21 + -20x + 5x2 = 14 + -11x + 3x2

Solving for variable 'x'.

Reorder the terms:
-21 + -14 + -20x + 11x + 5x2 + -3x2 = 14 + -11x + 3x2 + -14 + 11x + -3x2

Combine like terms: -21 + -14 = -35
-35 + -20x + 11x + 5x2 + -3x2 = 14 + -11x + 3x2 + -14 + 11x + -3x2

Combine like terms: -20x + 11x = -9x
-35 + -9x + 5x2 + -3x2 = 14 + -11x + 3x2 + -14 + 11x + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
-35 + -9x + 2x2 = 14 + -11x + 3x2 + -14 + 11x + -3x2

Reorder the terms:
-35 + -9x + 2x2 = 14 + -14 + -11x + 11x + 3x2 + -3x2

Combine like terms: 14 + -14 = 0
-35 + -9x + 2x2 = 0 + -11x + 11x + 3x2 + -3x2
-35 + -9x + 2x2 = -11x + 11x + 3x2 + -3x2

Combine like terms: -11x + 11x = 0
-35 + -9x + 2x2 = 0 + 3x2 + -3x2
-35 + -9x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-35 + -9x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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 = {-2.5, 7}

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