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

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


Simplifying
(2x + 5)(4x + -2) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)

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

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

Multiply (5 + 2x) * (-2 + 4x)
(5(-2 + 4x) + 2x * (-2 + 4x)) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)
((-2 * 5 + 4x * 5) + 2x * (-2 + 4x)) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)
((-10 + 20x) + 2x * (-2 + 4x)) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)
(-10 + 20x + (-2 * 2x + 4x * 2x)) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)
(-10 + 20x + (-4x + 8x2)) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)

Combine like terms: 20x + -4x = 16x
(-10 + 16x + 8x2) = (2x)(4x) + (2x)(-2) + (5)(4x) + (5)(-2)

Remove parenthesis around (2x)
-10 + 16x + 8x2 = 2x(4x) + (2x)(-2) + (5)(4x) + (5)(-2)

Remove parenthesis around (4x)
-10 + 16x + 8x2 = 2x * 4x + (2x)(-2) + (5)(4x) + (5)(-2)

Reorder the terms for easier multiplication:
-10 + 16x + 8x2 = 2 * 4x * x + (2x)(-2) + (5)(4x) + (5)(-2)

Multiply 2 * 4
-10 + 16x + 8x2 = 8x * x + (2x)(-2) + (5)(4x) + (5)(-2)

Multiply x * x
-10 + 16x + 8x2 = 8x2 + (2x)(-2) + (5)(4x) + (5)(-2)

Remove parenthesis around (2x)
-10 + 16x + 8x2 = 8x2 + 2x(-2) + (5)(4x) + (5)(-2)

Reorder the terms for easier multiplication:
-10 + 16x + 8x2 = 8x2 + 2 * -2x + (5)(4x) + (5)(-2)

Multiply 2 * -2
-10 + 16x + 8x2 = 8x2 + -4x + (5)(4x) + (5)(-2)

Remove parenthesis around (4x)
-10 + 16x + 8x2 = 8x2 + -4x + 5 * 4x + (5)(-2)

Multiply 5 * 4
-10 + 16x + 8x2 = 8x2 + -4x + 20x + (5)(-2)

Multiply 5 * -2
-10 + 16x + 8x2 = 8x2 + -4x + 20x + -10

Reorder the terms:
-10 + 16x + 8x2 = -10 + -4x + 20x + 8x2

Combine like terms: -4x + 20x = 16x
-10 + 16x + 8x2 = -10 + 16x + 8x2

Add '10' to each side of the equation.
-10 + 16x + 10 + 8x2 = -10 + 16x + 10 + 8x2

Reorder the terms:
-10 + 10 + 16x + 8x2 = -10 + 16x + 10 + 8x2

Combine like terms: -10 + 10 = 0
0 + 16x + 8x2 = -10 + 16x + 10 + 8x2
16x + 8x2 = -10 + 16x + 10 + 8x2

Reorder the terms:
16x + 8x2 = -10 + 10 + 16x + 8x2

Combine like terms: -10 + 10 = 0
16x + 8x2 = 0 + 16x + 8x2
16x + 8x2 = 16x + 8x2

Add '-16x' to each side of the equation.
16x + -16x + 8x2 = 16x + -16x + 8x2

Combine like terms: 16x + -16x = 0
0 + 8x2 = 16x + -16x + 8x2
8x2 = 16x + -16x + 8x2

Combine like terms: 16x + -16x = 0
8x2 = 0 + 8x2
8x2 = 8x2

Add '-8x2' to each side of the equation.
8x2 + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
0 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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