4x^2-10=3x^2-5x+4

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Solution for 4x^2-10=3x^2-5x+4 equation: 


Simplifying
4x2 + -10 = 3x2 + -5x + 4

Reorder the terms:
-10 + 4x2 = 3x2 + -5x + 4

Reorder the terms:
-10 + 4x2 = 4 + -5x + 3x2

Solving
-10 + 4x2 = 4 + -5x + 3x2

Solving for variable 'x'.

Reorder the terms:
-10 + -4 + 5x + 4x2 + -3x2 = 4 + -5x + 3x2 + -4 + 5x + -3x2

Combine like terms: -10 + -4 = -14
-14 + 5x + 4x2 + -3x2 = 4 + -5x + 3x2 + -4 + 5x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
-14 + 5x + 1x2 = 4 + -5x + 3x2 + -4 + 5x + -3x2

Reorder the terms:
-14 + 5x + 1x2 = 4 + -4 + -5x + 5x + 3x2 + -3x2

Combine like terms: 4 + -4 = 0
-14 + 5x + 1x2 = 0 + -5x + 5x + 3x2 + -3x2
-14 + 5x + 1x2 = -5x + 5x + 3x2 + -3x2

Combine like terms: -5x + 5x = 0
-14 + 5x + 1x2 = 0 + 3x2 + -3x2
-14 + 5x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + 5x + 1x2 = 0

Factor a trinomial.
(-7 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-7, 2}

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