(3x^2+5x-2)-(7x^2-5x+4)=

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Solution for (3x^2+5x-2)-(7x^2-5x+4)= equation:


Simplifying
(3x2 + 5x + -2) + -1(7x2 + -5x + 4) = 0

Reorder the terms:
(-2 + 5x + 3x2) + -1(7x2 + -5x + 4) = 0

Remove parenthesis around (-2 + 5x + 3x2)
-2 + 5x + 3x2 + -1(7x2 + -5x + 4) = 0

Reorder the terms:
-2 + 5x + 3x2 + -1(4 + -5x + 7x2) = 0
-2 + 5x + 3x2 + (4 * -1 + -5x * -1 + 7x2 * -1) = 0
-2 + 5x + 3x2 + (-4 + 5x + -7x2) = 0

Reorder the terms:
-2 + -4 + 5x + 5x + 3x2 + -7x2 = 0

Combine like terms: -2 + -4 = -6
-6 + 5x + 5x + 3x2 + -7x2 = 0

Combine like terms: 5x + 5x = 10x
-6 + 10x + 3x2 + -7x2 = 0

Combine like terms: 3x2 + -7x2 = -4x2
-6 + 10x + -4x2 = 0

Solving
-6 + 10x + -4x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5

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 = {1.5, 1}

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