(3x+1)(x+3)=19-2(x+2)(x+2)

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Solution for (3x+1)(x+3)=19-2(x+2)(x+2) equation:


Simplifying
(3x + 1)(x + 3) = 19 + -2(x + 2)(x + 2)

Reorder the terms:
(1 + 3x)(x + 3) = 19 + -2(x + 2)(x + 2)

Reorder the terms:
(1 + 3x)(3 + x) = 19 + -2(x + 2)(x + 2)

Multiply (1 + 3x) * (3 + x)
(1(3 + x) + 3x * (3 + x)) = 19 + -2(x + 2)(x + 2)
((3 * 1 + x * 1) + 3x * (3 + x)) = 19 + -2(x + 2)(x + 2)
((3 + 1x) + 3x * (3 + x)) = 19 + -2(x + 2)(x + 2)
(3 + 1x + (3 * 3x + x * 3x)) = 19 + -2(x + 2)(x + 2)
(3 + 1x + (9x + 3x2)) = 19 + -2(x + 2)(x + 2)

Combine like terms: 1x + 9x = 10x
(3 + 10x + 3x2) = 19 + -2(x + 2)(x + 2)

Reorder the terms:
3 + 10x + 3x2 = 19 + -2(2 + x)(x + 2)

Reorder the terms:
3 + 10x + 3x2 = 19 + -2(2 + x)(2 + x)

Multiply (2 + x) * (2 + x)
3 + 10x + 3x2 = 19 + -2(2(2 + x) + x(2 + x))
3 + 10x + 3x2 = 19 + -2((2 * 2 + x * 2) + x(2 + x))
3 + 10x + 3x2 = 19 + -2((4 + 2x) + x(2 + x))
3 + 10x + 3x2 = 19 + -2(4 + 2x + (2 * x + x * x))
3 + 10x + 3x2 = 19 + -2(4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
3 + 10x + 3x2 = 19 + -2(4 + 4x + x2)
3 + 10x + 3x2 = 19 + (4 * -2 + 4x * -2 + x2 * -2)
3 + 10x + 3x2 = 19 + (-8 + -8x + -2x2)

Combine like terms: 19 + -8 = 11
3 + 10x + 3x2 = 11 + -8x + -2x2

Solving
3 + 10x + 3x2 = 11 + -8x + -2x2

Solving for variable 'x'.

Reorder the terms:
3 + -11 + 10x + 8x + 3x2 + 2x2 = 11 + -8x + -2x2 + -11 + 8x + 2x2

Combine like terms: 3 + -11 = -8
-8 + 10x + 8x + 3x2 + 2x2 = 11 + -8x + -2x2 + -11 + 8x + 2x2

Combine like terms: 10x + 8x = 18x
-8 + 18x + 3x2 + 2x2 = 11 + -8x + -2x2 + -11 + 8x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
-8 + 18x + 5x2 = 11 + -8x + -2x2 + -11 + 8x + 2x2

Reorder the terms:
-8 + 18x + 5x2 = 11 + -11 + -8x + 8x + -2x2 + 2x2

Combine like terms: 11 + -11 = 0
-8 + 18x + 5x2 = 0 + -8x + 8x + -2x2 + 2x2
-8 + 18x + 5x2 = -8x + 8x + -2x2 + 2x2

Combine like terms: -8x + 8x = 0
-8 + 18x + 5x2 = 0 + -2x2 + 2x2
-8 + 18x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-8 + 18x + 5x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -5x) = 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 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4

Solution

x = {-4, 0.4}

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