8x^2+2x-21=2x^2+7x

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Solution for 8x^2+2x-21=2x^2+7x equation: 


Simplifying
8x2 + 2x + -21 = 2x2 + 7x

Reorder the terms:
-21 + 2x + 8x2 = 2x2 + 7x

Reorder the terms:
-21 + 2x + 8x2 = 7x + 2x2

Solving
-21 + 2x + 8x2 = 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-21 + 2x + -7x + 8x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: 2x + -7x = -5x
-21 + -5x + 8x2 + -2x2 = 7x + 2x2 + -7x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-21 + -5x + 6x2 = 7x + 2x2 + -7x + -2x2

Reorder the terms:
-21 + -5x + 6x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-21 + -5x + 6x2 = 0 + 2x2 + -2x2
-21 + -5x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-21 + -5x + 6x2 = 0

Factor a trinomial.
(-3 + -2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.5, 2.333333333}

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