(3x+1)(5x-3)=0

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Solution for (3x+1)(5x-3)=0 equation:


Simplifying
(3x + 1)(5x + -3) = 0

Reorder the terms:
(1 + 3x)(5x + -3) = 0

Reorder the terms:
(1 + 3x)(-3 + 5x) = 0

Multiply (1 + 3x) * (-3 + 5x)
(1(-3 + 5x) + 3x * (-3 + 5x)) = 0
((-3 * 1 + 5x * 1) + 3x * (-3 + 5x)) = 0
((-3 + 5x) + 3x * (-3 + 5x)) = 0
(-3 + 5x + (-3 * 3x + 5x * 3x)) = 0
(-3 + 5x + (-9x + 15x2)) = 0

Combine like terms: 5x + -9x = -4x
(-3 + -4x + 15x2) = 0

Solving
-3 + -4x + 15x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

Subproblem 2

Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 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 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Solution

x = {-0.3333333333, 0.6}

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