=(2x^2+3)(5)+(5x-2)(4x)

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Solution for =(2x^2+3)(5)+(5x-2)(4x) equation:


Simplifying
0 = (2x2 + 3)(5) + (5x + -2)(4x)

Reorder the terms:
0 = (3 + 2x2)(5) + (5x + -2)(4x)

Reorder the terms for easier multiplication:
0 = 5(3 + 2x2) + (5x + -2)(4x)
0 = (3 * 5 + 2x2 * 5) + (5x + -2)(4x)
0 = (15 + 10x2) + (5x + -2)(4x)

Reorder the terms:
0 = 15 + 10x2 + (-2 + 5x)(4x)

Remove parenthesis around (4x)
0 = 15 + 10x2 + (-2 + 5x) * 4x

Reorder the terms for easier multiplication:
0 = 15 + 10x2 + 4x(-2 + 5x)
0 = 15 + 10x2 + (-2 * 4x + 5x * 4x)
0 = 15 + 10x2 + (-8x + 20x2)

Reorder the terms:
0 = 15 + -8x + 10x2 + 20x2

Combine like terms: 10x2 + 20x2 = 30x2
0 = 15 + -8x + 30x2

Solving
0 = 15 + -8x + 30x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 8x + -30x2 = 15 + -8x + 30x2 + -15 + 8x + -30x2

Reorder the terms:
-15 + 8x + -30x2 = 15 + -15 + -8x + 8x + 30x2 + -30x2

Combine like terms: 15 + -15 = 0
-15 + 8x + -30x2 = 0 + -8x + 8x + 30x2 + -30x2
-15 + 8x + -30x2 = -8x + 8x + 30x2 + -30x2

Combine like terms: -8x + 8x = 0
-15 + 8x + -30x2 = 0 + 30x2 + -30x2
-15 + 8x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
-15 + 8x + -30x2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
0.5 + -0.2666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.2666666667x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.2666666667x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.2666666667x + x2 = 0 + -0.5
-0.2666666667x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.2666666667x + x2 = -0.5

The x term is -0.2666666667x.  Take half its coefficient (-0.1333333334).
Square it (0.01777777780) and add it to both sides.

Add '0.01777777780' to each side of the equation.
-0.2666666667x + 0.01777777780 + x2 = -0.5 + 0.01777777780

Reorder the terms:
0.01777777780 + -0.2666666667x + x2 = -0.5 + 0.01777777780

Combine like terms: -0.5 + 0.01777777780 = -0.4822222222
0.01777777780 + -0.2666666667x + x2 = -0.4822222222

Factor a perfect square on the left side:
(x + -0.1333333334)(x + -0.1333333334) = -0.4822222222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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