3+(2x+3)(4x-1)=10(2x^2+x)+12x

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Solution for 3+(2x+3)(4x-1)=10(2x^2+x)+12x equation: 


Simplifying
3 + (2x + 3)(4x + -1) = 10(2x2 + x) + 12x

Reorder the terms:
3 + (3 + 2x)(4x + -1) = 10(2x2 + x) + 12x

Reorder the terms:
3 + (3 + 2x)(-1 + 4x) = 10(2x2 + x) + 12x

Multiply (3 + 2x) * (-1 + 4x)
3 + (3(-1 + 4x) + 2x * (-1 + 4x)) = 10(2x2 + x) + 12x
3 + ((-1 * 3 + 4x * 3) + 2x * (-1 + 4x)) = 10(2x2 + x) + 12x
3 + ((-3 + 12x) + 2x * (-1 + 4x)) = 10(2x2 + x) + 12x
3 + (-3 + 12x + (-1 * 2x + 4x * 2x)) = 10(2x2 + x) + 12x
3 + (-3 + 12x + (-2x + 8x2)) = 10(2x2 + x) + 12x

Combine like terms: 12x + -2x = 10x
3 + (-3 + 10x + 8x2) = 10(2x2 + x) + 12x

Combine like terms: 3 + -3 = 0
0 + 10x + 8x2 = 10(2x2 + x) + 12x
10x + 8x2 = 10(2x2 + x) + 12x

Reorder the terms:
10x + 8x2 = 10(x + 2x2) + 12x
10x + 8x2 = (x * 10 + 2x2 * 10) + 12x
10x + 8x2 = (10x + 20x2) + 12x

Reorder the terms:
10x + 8x2 = 10x + 12x + 20x2

Combine like terms: 10x + 12x = 22x
10x + 8x2 = 22x + 20x2

Solving
10x + 8x2 = 22x + 20x2

Solving for variable 'x'.

Reorder the terms:
10x + -22x + 8x2 + -20x2 = 22x + 20x2 + -22x + -20x2

Combine like terms: 10x + -22x = -12x
-12x + 8x2 + -20x2 = 22x + 20x2 + -22x + -20x2

Combine like terms: 8x2 + -20x2 = -12x2
-12x + -12x2 = 22x + 20x2 + -22x + -20x2

Reorder the terms:
-12x + -12x2 = 22x + -22x + 20x2 + -20x2

Combine like terms: 22x + -22x = 0
-12x + -12x2 = 0 + 20x2 + -20x2
-12x + -12x2 = 20x2 + -20x2

Combine like terms: 20x2 + -20x2 = 0
-12x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-12x'.
-12x(1 + x) = 0

Ignore the factor -12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {0, -1}

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