2x^2-3x=-4x^2-12x-3

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Solution for 2x^2-3x=-4x^2-12x-3 equation:


Simplifying
2x2 + -3x = -4x2 + -12x + -3

Reorder the terms:
-3x + 2x2 = -4x2 + -12x + -3

Reorder the terms:
-3x + 2x2 = -3 + -12x + -4x2

Solving
-3x + 2x2 = -3 + -12x + -4x2

Solving for variable 'x'.

Reorder the terms:
3 + -3x + 12x + 2x2 + 4x2 = -3 + -12x + -4x2 + 3 + 12x + 4x2

Combine like terms: -3x + 12x = 9x
3 + 9x + 2x2 + 4x2 = -3 + -12x + -4x2 + 3 + 12x + 4x2

Combine like terms: 2x2 + 4x2 = 6x2
3 + 9x + 6x2 = -3 + -12x + -4x2 + 3 + 12x + 4x2

Reorder the terms:
3 + 9x + 6x2 = -3 + 3 + -12x + 12x + -4x2 + 4x2

Combine like terms: -3 + 3 = 0
3 + 9x + 6x2 = 0 + -12x + 12x + -4x2 + 4x2
3 + 9x + 6x2 = -12x + 12x + -4x2 + 4x2

Combine like terms: -12x + 12x = 0
3 + 9x + 6x2 = 0 + -4x2 + 4x2
3 + 9x + 6x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
3 + 9x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3x + 2x2) = 0

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

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5

Solution

x = {-1, -0.5}

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