(x+3)(5x+1)=(2x+1)(x+7)

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Solution for (x+3)(5x+1)=(2x+1)(x+7) equation:


Simplifying
(x + 3)(5x + 1) = (2x + 1)(x + 7)

Reorder the terms:
(3 + x)(5x + 1) = (2x + 1)(x + 7)

Reorder the terms:
(3 + x)(1 + 5x) = (2x + 1)(x + 7)

Multiply (3 + x) * (1 + 5x)
(3(1 + 5x) + x(1 + 5x)) = (2x + 1)(x + 7)
((1 * 3 + 5x * 3) + x(1 + 5x)) = (2x + 1)(x + 7)
((3 + 15x) + x(1 + 5x)) = (2x + 1)(x + 7)
(3 + 15x + (1 * x + 5x * x)) = (2x + 1)(x + 7)
(3 + 15x + (1x + 5x2)) = (2x + 1)(x + 7)

Combine like terms: 15x + 1x = 16x
(3 + 16x + 5x2) = (2x + 1)(x + 7)

Reorder the terms:
3 + 16x + 5x2 = (1 + 2x)(x + 7)

Reorder the terms:
3 + 16x + 5x2 = (1 + 2x)(7 + x)

Multiply (1 + 2x) * (7 + x)
3 + 16x + 5x2 = (1(7 + x) + 2x * (7 + x))
3 + 16x + 5x2 = ((7 * 1 + x * 1) + 2x * (7 + x))
3 + 16x + 5x2 = ((7 + 1x) + 2x * (7 + x))
3 + 16x + 5x2 = (7 + 1x + (7 * 2x + x * 2x))
3 + 16x + 5x2 = (7 + 1x + (14x + 2x2))

Combine like terms: 1x + 14x = 15x
3 + 16x + 5x2 = (7 + 15x + 2x2)

Solving
3 + 16x + 5x2 = 7 + 15x + 2x2

Solving for variable 'x'.

Reorder the terms:
3 + -7 + 16x + -15x + 5x2 + -2x2 = 7 + 15x + 2x2 + -7 + -15x + -2x2

Combine like terms: 3 + -7 = -4
-4 + 16x + -15x + 5x2 + -2x2 = 7 + 15x + 2x2 + -7 + -15x + -2x2

Combine like terms: 16x + -15x = 1x
-4 + 1x + 5x2 + -2x2 = 7 + 15x + 2x2 + -7 + -15x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
-4 + 1x + 3x2 = 7 + 15x + 2x2 + -7 + -15x + -2x2

Reorder the terms:
-4 + 1x + 3x2 = 7 + -7 + 15x + -15x + 2x2 + -2x2

Combine like terms: 7 + -7 = 0
-4 + 1x + 3x2 = 0 + 15x + -15x + 2x2 + -2x2
-4 + 1x + 3x2 = 15x + -15x + 2x2 + -2x2

Combine like terms: 15x + -15x = 0
-4 + 1x + 3x2 = 0 + 2x2 + -2x2
-4 + 1x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 1x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(1 + -1x) = 0

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

Subproblem 2

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {-1.333333333, 1}

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