x(2x+3)=5(2x+3)

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


Simplifying
x(2x + 3) = 5(2x + 3)

Reorder the terms:
x(3 + 2x) = 5(2x + 3)
(3 * x + 2x * x) = 5(2x + 3)
(3x + 2x2) = 5(2x + 3)

Reorder the terms:
3x + 2x2 = 5(3 + 2x)
3x + 2x2 = (3 * 5 + 2x * 5)
3x + 2x2 = (15 + 10x)

Solving
3x + 2x2 = 15 + 10x

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + -10x + 2x2 = 15 + 10x + -15 + -10x

Combine like terms: 3x + -10x = -7x
-15 + -7x + 2x2 = 15 + 10x + -15 + -10x

Reorder the terms:
-15 + -7x + 2x2 = 15 + -15 + 10x + -10x

Combine like terms: 15 + -15 = 0
-15 + -7x + 2x2 = 0 + 10x + -10x
-15 + -7x + 2x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-15 + -7x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -1x) = 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-1.5, 5}

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