8x^2+10=2x^2+23x-10

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Solution for 8x^2+10=2x^2+23x-10 equation: 


Simplifying
8x2 + 10 = 2x2 + 23x + -10

Reorder the terms:
10 + 8x2 = 2x2 + 23x + -10

Reorder the terms:
10 + 8x2 = -10 + 23x + 2x2

Solving
10 + 8x2 = -10 + 23x + 2x2

Solving for variable 'x'.

Reorder the terms:
10 + 10 + -23x + 8x2 + -2x2 = -10 + 23x + 2x2 + 10 + -23x + -2x2

Combine like terms: 10 + 10 = 20
20 + -23x + 8x2 + -2x2 = -10 + 23x + 2x2 + 10 + -23x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
20 + -23x + 6x2 = -10 + 23x + 2x2 + 10 + -23x + -2x2

Reorder the terms:
20 + -23x + 6x2 = -10 + 10 + 23x + -23x + 2x2 + -2x2

Combine like terms: -10 + 10 = 0
20 + -23x + 6x2 = 0 + 23x + -23x + 2x2 + -2x2
20 + -23x + 6x2 = 23x + -23x + 2x2 + -2x2

Combine like terms: 23x + -23x = 0
20 + -23x + 6x2 = 0 + 2x2 + -2x2
20 + -23x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + -23x + 6x2 = 0

Factor a trinomial.
(4 + -3x)(5 + -2x) = 0


Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
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
Solution
x = {1.333333333, 2.5}

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