x^2+3x=4x+12

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


Simplifying
x2 + 3x = 4x + 12

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

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

Solving
3x + x2 = 12 + 4x

Solving for variable 'x'.

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

Combine like terms: 3x + -4x = -1x
-12 + -1x + x2 = 12 + 4x + -12 + -4x

Reorder the terms:
-12 + -1x + x2 = 12 + -12 + 4x + -4x

Combine like terms: 12 + -12 = 0
-12 + -1x + x2 = 0 + 4x + -4x
-12 + -1x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0

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 '(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 = {-3, 4}

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