2x^2+3x-15=-4x^2-6x

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Solution for 2x^2+3x-15=-4x^2-6x equation:


Simplifying
2x2 + 3x + -15 = -4x2 + -6x

Reorder the terms:
-15 + 3x + 2x2 = -4x2 + -6x

Reorder the terms:
-15 + 3x + 2x2 = -6x + -4x2

Solving
-15 + 3x + 2x2 = -6x + -4x2

Solving for variable 'x'.

Reorder the terms:
-15 + 3x + 6x + 2x2 + 4x2 = -6x + -4x2 + 6x + 4x2

Combine like terms: 3x + 6x = 9x
-15 + 9x + 2x2 + 4x2 = -6x + -4x2 + 6x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
-15 + 9x + 6x2 = -6x + -4x2 + 6x + 4x2

Reorder the terms:
-15 + 9x + 6x2 = -6x + 6x + -4x2 + 4x2

Combine like terms: -6x + 6x = 0
-15 + 9x + 6x2 = 0 + -4x2 + 4x2
-15 + 9x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15 + 9x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 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 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5

Subproblem 2

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

Solution

x = {-2.5, 1}

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