4(x^2)-32=3(x^2)-4x

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Solution for 4(x^2)-32=3(x^2)-4x equation:


Simplifying
4(x2) + -32 = 3(x2) + -4x

Reorder the terms:
-32 + 4x2 = 3(x2) + -4x

Reorder the terms:
-32 + 4x2 = -4x + 3x2

Solving
-32 + 4x2 = -4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-32 + 4x + 4x2 + -3x2 = -4x + 3x2 + 4x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-32 + 4x + 1x2 = -4x + 3x2 + 4x + -3x2

Reorder the terms:
-32 + 4x + 1x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-32 + 4x + 1x2 = 0 + 3x2 + -3x2
-32 + 4x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-32 + 4x + 1x2 = 0

Factor a trinomial.
(-8 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8

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 = {-8, 4}

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