(5x+1)(9x+3)=-2(5x+1)

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Solution for (5x+1)(9x+3)=-2(5x+1) equation:


Simplifying
(5x + 1)(9x + 3) = -2(5x + 1)

Reorder the terms:
(1 + 5x)(9x + 3) = -2(5x + 1)

Reorder the terms:
(1 + 5x)(3 + 9x) = -2(5x + 1)

Multiply (1 + 5x) * (3 + 9x)
(1(3 + 9x) + 5x * (3 + 9x)) = -2(5x + 1)
((3 * 1 + 9x * 1) + 5x * (3 + 9x)) = -2(5x + 1)
((3 + 9x) + 5x * (3 + 9x)) = -2(5x + 1)
(3 + 9x + (3 * 5x + 9x * 5x)) = -2(5x + 1)
(3 + 9x + (15x + 45x2)) = -2(5x + 1)

Combine like terms: 9x + 15x = 24x
(3 + 24x + 45x2) = -2(5x + 1)

Reorder the terms:
3 + 24x + 45x2 = -2(1 + 5x)
3 + 24x + 45x2 = (1 * -2 + 5x * -2)
3 + 24x + 45x2 = (-2 + -10x)

Solving
3 + 24x + 45x2 = -2 + -10x

Solving for variable 'x'.

Reorder the terms:
3 + 2 + 24x + 10x + 45x2 = -2 + -10x + 2 + 10x

Combine like terms: 3 + 2 = 5
5 + 24x + 10x + 45x2 = -2 + -10x + 2 + 10x

Combine like terms: 24x + 10x = 34x
5 + 34x + 45x2 = -2 + -10x + 2 + 10x

Reorder the terms:
5 + 34x + 45x2 = -2 + 2 + -10x + 10x

Combine like terms: -2 + 2 = 0
5 + 34x + 45x2 = 0 + -10x + 10x
5 + 34x + 45x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
5 + 34x + 45x2 = 0

Factor a trinomial.
(5 + 9x)(1 + 5x) = 0

Subproblem 1

Set the factor '(5 + 9x)' equal to zero and attempt to solve: Simplifying 5 + 9x = 0 Solving 5 + 9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 9x = 0 + -5 9x = 0 + -5 Combine like terms: 0 + -5 = -5 9x = -5 Divide each side by '9'. x = -0.5555555556 Simplifying x = -0.5555555556

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 = {-0.5555555556, -0.2}

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