(2x+5)(2x-1)=3x^2+6x+3

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Solution for (2x+5)(2x-1)=3x^2+6x+3 equation: 


Simplifying
(2x + 5)(2x + -1) = 3x2 + 6x + 3

Reorder the terms:
(5 + 2x)(2x + -1) = 3x2 + 6x + 3

Reorder the terms:
(5 + 2x)(-1 + 2x) = 3x2 + 6x + 3

Multiply (5 + 2x) * (-1 + 2x)
(5(-1 + 2x) + 2x * (-1 + 2x)) = 3x2 + 6x + 3
((-1 * 5 + 2x * 5) + 2x * (-1 + 2x)) = 3x2 + 6x + 3
((-5 + 10x) + 2x * (-1 + 2x)) = 3x2 + 6x + 3
(-5 + 10x + (-1 * 2x + 2x * 2x)) = 3x2 + 6x + 3
(-5 + 10x + (-2x + 4x2)) = 3x2 + 6x + 3

Combine like terms: 10x + -2x = 8x
(-5 + 8x + 4x2) = 3x2 + 6x + 3

Reorder the terms:
-5 + 8x + 4x2 = 3 + 6x + 3x2

Solving
-5 + 8x + 4x2 = 3 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
-5 + -3 + 8x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: -5 + -3 = -8
-8 + 8x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: 8x + -6x = 2x
-8 + 2x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-8 + 2x + 1x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Reorder the terms:
-8 + 2x + 1x2 = 3 + -3 + 6x + -6x + 3x2 + -3x2

Combine like terms: 3 + -3 = 0
-8 + 2x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2
-8 + 2x + 1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-8 + 2x + 1x2 = 0 + 3x2 + -3x2
-8 + 2x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-8 + 2x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -1x) = 0


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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}

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