2x^2=8(4x-5)+10

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Solution for 2x^2=8(4x-5)+10 equation: 


Simplifying
2x2 = 8(4x + -5) + 10

Reorder the terms:
2x2 = 8(-5 + 4x) + 10
2x2 = (-5 * 8 + 4x * 8) + 10
2x2 = (-40 + 32x) + 10

Reorder the terms:
2x2 = -40 + 10 + 32x

Combine like terms: -40 + 10 = -30
2x2 = -30 + 32x

Solving
2x2 = -30 + 32x

Solving for variable 'x'.

Reorder the terms:
30 + -32x + 2x2 = -30 + 32x + 30 + -32x

Reorder the terms:
30 + -32x + 2x2 = -30 + 30 + 32x + -32x

Combine like terms: -30 + 30 = 0
30 + -32x + 2x2 = 0 + 32x + -32x
30 + -32x + 2x2 = 32x + -32x

Combine like terms: 32x + -32x = 0
30 + -32x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -16x + x2) = 0

Factor a trinomial.
2((1 + -1x)(15 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1

Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {1, 15}

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