(2x-5)(7x+3)=0

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Solution for (2x-5)(7x+3)=0 equation:


Simplifying
(2x + -5)(7x + 3) = 0

Reorder the terms:
(-5 + 2x)(7x + 3) = 0

Reorder the terms:
(-5 + 2x)(3 + 7x) = 0

Multiply (-5 + 2x) * (3 + 7x)
(-5(3 + 7x) + 2x * (3 + 7x)) = 0
((3 * -5 + 7x * -5) + 2x * (3 + 7x)) = 0
((-15 + -35x) + 2x * (3 + 7x)) = 0
(-15 + -35x + (3 * 2x + 7x * 2x)) = 0
(-15 + -35x + (6x + 14x2)) = 0

Combine like terms: -35x + 6x = -29x
(-15 + -29x + 14x2) = 0

Solving
-15 + -29x + 14x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -7x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -7x)' equal to zero and attempt to solve: Simplifying -3 + -7x = 0 Solving -3 + -7x = 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 + -7x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7x = 0 + 3 -7x = 0 + 3 Combine like terms: 0 + 3 = 3 -7x = 3 Divide each side by '-7'. x = -0.4285714286 Simplifying x = -0.4285714286

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-0.4285714286, 2.5}

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