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

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


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

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

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

Multiply (3 + 2x) * (-7 + 5x)
(3(-7 + 5x) + 2x * (-7 + 5x)) = 0
((-7 * 3 + 5x * 3) + 2x * (-7 + 5x)) = 0
((-21 + 15x) + 2x * (-7 + 5x)) = 0
(-21 + 15x + (-7 * 2x + 5x * 2x)) = 0
(-21 + 15x + (-14x + 10x2)) = 0

Combine like terms: 15x + -14x = 1x
(-21 + 1x + 10x2) = 0

Solving
-21 + 1x + 10x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5

Subproblem 2

Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4

Solution

x = {-1.5, 1.4}

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