4X^2-9X+10=10-25X

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Solution for 4X^2-9X+10=10-25X equation: 


Simplifying
4X2 + -9X + 10 = 10 + -25X

Reorder the terms:
10 + -9X + 4X2 = 10 + -25X

Add '-10' to each side of the equation.
10 + -9X + -10 + 4X2 = 10 + -10 + -25X

Reorder the terms:
10 + -10 + -9X + 4X2 = 10 + -10 + -25X

Combine like terms: 10 + -10 = 0
0 + -9X + 4X2 = 10 + -10 + -25X
-9X + 4X2 = 10 + -10 + -25X

Combine like terms: 10 + -10 = 0
-9X + 4X2 = 0 + -25X
-9X + 4X2 = -25X

Solving
-9X + 4X2 = -25X

Solving for variable 'X'.

Reorder the terms:
-9X + 25X + 4X2 = -25X + 25X

Combine like terms: -9X + 25X = 16X
16X + 4X2 = -25X + 25X

Combine like terms: -25X + 25X = 0
16X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '4X'.
4X(4 + X) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0

Subproblem 2
Set the factor '(4 + X)' equal to zero and attempt to solve:

Simplifying
4 + X = 0

Solving
4 + X = 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 + X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + X = 0 + -4
X = 0 + -4

Combine like terms: 0 + -4 = -4
X = -4

Simplifying
X = -4
Solution
X = {0, -4}

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