(5x+7)(7x-4)=0

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Solution for (5x+7)(7x-4)=0 equation:


Simplifying
(5x + 7)(7x + -4) = 0

Reorder the terms:
(7 + 5x)(7x + -4) = 0

Reorder the terms:
(7 + 5x)(-4 + 7x) = 0

Multiply (7 + 5x) * (-4 + 7x)
(7(-4 + 7x) + 5x * (-4 + 7x)) = 0
((-4 * 7 + 7x * 7) + 5x * (-4 + 7x)) = 0
((-28 + 49x) + 5x * (-4 + 7x)) = 0
(-28 + 49x + (-4 * 5x + 7x * 5x)) = 0
(-28 + 49x + (-20x + 35x2)) = 0

Combine like terms: 49x + -20x = 29x
(-28 + 29x + 35x2) = 0

Solving
-28 + 29x + 35x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -5x)(4 + -7x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -7x)' equal to zero and attempt to solve: Simplifying 4 + -7x = 0 Solving 4 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7x = 0 + -4 -7x = 0 + -4 Combine like terms: 0 + -4 = -4 -7x = -4 Divide each side by '-7'. x = 0.5714285714 Simplifying x = 0.5714285714

Solution

x = {-1.4, 0.5714285714}

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