(5x-7)(2x+6)=0

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Solution for (5x-7)(2x+6)=0 equation:


Simplifying
(5x + -7)(2x + 6) = 0

Reorder the terms:
(-7 + 5x)(2x + 6) = 0

Reorder the terms:
(-7 + 5x)(6 + 2x) = 0

Multiply (-7 + 5x) * (6 + 2x)
(-7(6 + 2x) + 5x * (6 + 2x)) = 0
((6 * -7 + 2x * -7) + 5x * (6 + 2x)) = 0
((-42 + -14x) + 5x * (6 + 2x)) = 0
(-42 + -14x + (6 * 5x + 2x * 5x)) = 0
(-42 + -14x + (30x + 10x2)) = 0

Combine like terms: -14x + 30x = 16x
(-42 + 16x + 10x2) = 0

Solving
-42 + 16x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 8x + 5x2) = 0

Factor a trinomial.
2((-3 + -1x)(7 + -5x)) = 0

Ignore the factor 2.

Subproblem 1

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

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 = {-3, 1.4}

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