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

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


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

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

Multiply (2 + 5x) * (7 + -2x)
(2(7 + -2x) + 5x * (7 + -2x)) = 0
((7 * 2 + -2x * 2) + 5x * (7 + -2x)) = 0
((14 + -4x) + 5x * (7 + -2x)) = 0
(14 + -4x + (7 * 5x + -2x * 5x)) = 0
(14 + -4x + (35x + -10x2)) = 0

Combine like terms: -4x + 35x = 31x
(14 + 31x + -10x2) = 0

Solving
14 + 31x + -10x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(7 + -2x)' equal to zero and attempt to solve: Simplifying 7 + -2x = 0 Solving 7 + -2x = 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 + -2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2x = 0 + -7 -2x = 0 + -7 Combine like terms: 0 + -7 = -7 -2x = -7 Divide each side by '-2'. x = 3.5 Simplifying x = 3.5

Subproblem 2

Set the factor '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Divide each side by '5'. x = -0.4 Simplifying x = -0.4

Solution

x = {3.5, -0.4}

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