7x^2-15x+11=2x^2-3x+4

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Solution for 7x^2-15x+11=2x^2-3x+4 equation: 


Simplifying
7x2 + -15x + 11 = 2x2 + -3x + 4

Reorder the terms:
11 + -15x + 7x2 = 2x2 + -3x + 4

Reorder the terms:
11 + -15x + 7x2 = 4 + -3x + 2x2

Solving
11 + -15x + 7x2 = 4 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
11 + -4 + -15x + 3x + 7x2 + -2x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Combine like terms: 11 + -4 = 7
7 + -15x + 3x + 7x2 + -2x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Combine like terms: -15x + 3x = -12x
7 + -12x + 7x2 + -2x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Combine like terms: 7x2 + -2x2 = 5x2
7 + -12x + 5x2 = 4 + -3x + 2x2 + -4 + 3x + -2x2

Reorder the terms:
7 + -12x + 5x2 = 4 + -4 + -3x + 3x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
7 + -12x + 5x2 = 0 + -3x + 3x + 2x2 + -2x2
7 + -12x + 5x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
7 + -12x + 5x2 = 0 + 2x2 + -2x2
7 + -12x + 5x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7 + -12x + 5x2 = 0

Factor a trinomial.
(1 + -1x)(7 + -5x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {1, 1.4}

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