(2x+5)(5x-7)=(3x+1)(13)

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Solution for (2x+5)(5x-7)=(3x+1)(13) equation:


Simplifying
(2x + 5)(5x + -7) = (3x + 1)(13)

Reorder the terms:
(5 + 2x)(5x + -7) = (3x + 1)(13)

Reorder the terms:
(5 + 2x)(-7 + 5x) = (3x + 1)(13)

Multiply (5 + 2x) * (-7 + 5x)
(5(-7 + 5x) + 2x * (-7 + 5x)) = (3x + 1)(13)
((-7 * 5 + 5x * 5) + 2x * (-7 + 5x)) = (3x + 1)(13)
((-35 + 25x) + 2x * (-7 + 5x)) = (3x + 1)(13)
(-35 + 25x + (-7 * 2x + 5x * 2x)) = (3x + 1)(13)
(-35 + 25x + (-14x + 10x2)) = (3x + 1)(13)

Combine like terms: 25x + -14x = 11x
(-35 + 11x + 10x2) = (3x + 1)(13)

Reorder the terms:
-35 + 11x + 10x2 = (1 + 3x)(13)

Reorder the terms for easier multiplication:
-35 + 11x + 10x2 = 13(1 + 3x)
-35 + 11x + 10x2 = (1 * 13 + 3x * 13)
-35 + 11x + 10x2 = (13 + 39x)

Solving
-35 + 11x + 10x2 = 13 + 39x

Solving for variable 'x'.

Reorder the terms:
-35 + -13 + 11x + -39x + 10x2 = 13 + 39x + -13 + -39x

Combine like terms: -35 + -13 = -48
-48 + 11x + -39x + 10x2 = 13 + 39x + -13 + -39x

Combine like terms: 11x + -39x = -28x
-48 + -28x + 10x2 = 13 + 39x + -13 + -39x

Reorder the terms:
-48 + -28x + 10x2 = 13 + -13 + 39x + -39x

Combine like terms: 13 + -13 = 0
-48 + -28x + 10x2 = 0 + 39x + -39x
-48 + -28x + 10x2 = 39x + -39x

Combine like terms: 39x + -39x = 0
-48 + -28x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -14x + 5x2) = 0

Factor a trinomial.
2((-6 + -5x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-1.2, 4}

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