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

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


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

Reorder the terms:
3(1 + 5x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2)
(1 * 3 + 5x * 3) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2)
(3 + 15x) + (5x + 1)(5x + 1) = (5x + 1)(3x + -2)

Reorder the terms:
3 + 15x + (1 + 5x)(5x + 1) = (5x + 1)(3x + -2)

Reorder the terms:
3 + 15x + (1 + 5x)(1 + 5x) = (5x + 1)(3x + -2)

Multiply (1 + 5x) * (1 + 5x)
3 + 15x + (1(1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -2)
3 + 15x + ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) = (5x + 1)(3x + -2)
3 + 15x + ((1 + 5x) + 5x * (1 + 5x)) = (5x + 1)(3x + -2)
3 + 15x + (1 + 5x + (1 * 5x + 5x * 5x)) = (5x + 1)(3x + -2)
3 + 15x + (1 + 5x + (5x + 25x2)) = (5x + 1)(3x + -2)

Combine like terms: 5x + 5x = 10x
3 + 15x + (1 + 10x + 25x2) = (5x + 1)(3x + -2)

Reorder the terms:
3 + 1 + 15x + 10x + 25x2 = (5x + 1)(3x + -2)

Combine like terms: 3 + 1 = 4
4 + 15x + 10x + 25x2 = (5x + 1)(3x + -2)

Combine like terms: 15x + 10x = 25x
4 + 25x + 25x2 = (5x + 1)(3x + -2)

Reorder the terms:
4 + 25x + 25x2 = (1 + 5x)(3x + -2)

Reorder the terms:
4 + 25x + 25x2 = (1 + 5x)(-2 + 3x)

Multiply (1 + 5x) * (-2 + 3x)
4 + 25x + 25x2 = (1(-2 + 3x) + 5x * (-2 + 3x))
4 + 25x + 25x2 = ((-2 * 1 + 3x * 1) + 5x * (-2 + 3x))
4 + 25x + 25x2 = ((-2 + 3x) + 5x * (-2 + 3x))
4 + 25x + 25x2 = (-2 + 3x + (-2 * 5x + 3x * 5x))
4 + 25x + 25x2 = (-2 + 3x + (-10x + 15x2))

Combine like terms: 3x + -10x = -7x
4 + 25x + 25x2 = (-2 + -7x + 15x2)

Solving
4 + 25x + 25x2 = -2 + -7x + 15x2

Solving for variable 'x'.

Reorder the terms:
4 + 2 + 25x + 7x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2

Combine like terms: 4 + 2 = 6
6 + 25x + 7x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2

Combine like terms: 25x + 7x = 32x
6 + 32x + 25x2 + -15x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2

Combine like terms: 25x2 + -15x2 = 10x2
6 + 32x + 10x2 = -2 + -7x + 15x2 + 2 + 7x + -15x2

Reorder the terms:
6 + 32x + 10x2 = -2 + 2 + -7x + 7x + 15x2 + -15x2

Combine like terms: -2 + 2 = 0
6 + 32x + 10x2 = 0 + -7x + 7x + 15x2 + -15x2
6 + 32x + 10x2 = -7x + 7x + 15x2 + -15x2

Combine like terms: -7x + 7x = 0
6 + 32x + 10x2 = 0 + 15x2 + -15x2
6 + 32x + 10x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
6 + 32x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 16x + 5x2) = 0

Factor a trinomial.
2((3 + x)(1 + 5x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(1 + 5x)' equal to zero and attempt to solve: Simplifying 1 + 5x = 0 Solving 1 + 5x = 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 + 5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5x = 0 + -1 5x = 0 + -1 Combine like terms: 0 + -1 = -1 5x = -1 Divide each side by '5'. x = -0.2 Simplifying x = -0.2

Solution

x = {-3, -0.2}

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